Algebra Books

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We have compiled the list of Best Reference Books on Algebra subject. These books are used by students of top universities, institutes and colleges. Here is the full list of best books on Algebra along with reviews.

Kindly note that we have put a lot of effort into researching the best books on Algebra subject and came out with a recommended list of best books. The table below contains the Name of these best books, their authors, publishers and an unbiased review of books on “Algebra” as well as links to the Amazon website to directly purchase these books. As an Amazon Associate, we earn from qualifying purchases, but this does not impact our reviews, comparisons, and listing of these top books; the table serves as a ready reckoner list of these best books.

List of Algebra Books with author’s names, publishers, and an unbiased review as well as links to the Amazon website to directly purchase these books.

1. Basic Algebra

1. “Complex Variables and Applications” by R V Churchill and J W Brown

“Complex Variables and Applications” Book Review: The book is written from a theoretical as well as practical point-of-view and presents a clear introduction of complex variables. The initial chapters of the feature complex numbers, analytical functions, elementary functions, integrals, series, residues and poles, applications of residues, and mapping by elementary functions. The remaining chapters describe conformal mapping, applications of conformal mapping, Schwarz-Christoffel transformation, and integral formulas of the Poisson types in detail. The applications of complex variables as well as the featured topics in various fields and subjects are illustrated.

2. “Applied and Computational Complex Analysis Vol.I” by P Henrici

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“Applied and Computational Complex Analysis Vol.I” Book Review: The book is a balanced piece of writing featuring both basic theory and practical applications of analytic functions of one or several complex variables. The chapters of this book cover all the major topics related to formal power series, function analytic at a point, analytic continuation, complex navigation, conformal mapping, polynomials, and partial fractions. The solutions of algebraic and transcendental equations are discussed in detail. Each chapter ends with a section of notes and assignments for self-study and self-assessment of the readers.

3. “Applied and Computational Complex Analysis Vol.II” by P Henrici

“Applied and Computational Complex Analysis Vol.II” Book Review: The book is an excellent blend of fundamental theory and practical applications of complex analysis. The chapters of this revolves around infinite products, ordinary differential equations, special functions, integral transforms, asymptotic methods, and continued fractions. The book is enriched with several notes and assignments. Many problems are featured throughout the text for better understanding and practice of the readers. The book concludes with a bibliography and an appendix featuring some additional problems.

4. “Basic Algebra I” by Nathan Jacobson

“Basic Algebra I” Book Review: The book presents both conceptual as well as theoretical aspects of basic algebra. The chapters of this book contain a detailed description of set theory, group theory, rings, modules, Galois theory, polynomials, linear algebra, and associative algebra are discussed in detail. Moving further, the advanced topics like Lie and Jordan algebras, lattices, and Boolean algebras are thoroughly explained. The book also features intuitive and precisely explained proofs. Several exercises are included in this textbook. The book will be suitable for the undergraduate students of mathematics.

5. “Algebra – The Very Basics” by Metin Bektas

“Algebra – The Very Basics” Book Review: The book is intended for beginners in the field of algebra and hence features algebra from its very basics. The chapters of this book cover all the major topics and concepts underlying exponents, brackets, linear equations, and quadratic equations. The book is a well-structured and comprehensive piece of writing. The chapters are precise and easy-to-understand. The topics featured in this book are efficiently explained with the help of suitable examples. For providing a strong foundation to the beginners, many exercises along with their solutions are inserted in this text. The individuals interested in calculus and mathematical physics will find this text valuable.

6. “Practical Algebra: A Self-Teaching Guide” by Peter H Selby and Steve Slavin

“Practical Algebra: A Self-Teaching Guide” Book Review: The book introduces readers to the fundamental aspects and applications of algebra in problem solving. It begins with a detailed description of the number system. The chapters of this book broadly cover monomials and polynomials, factoring algebraic expressions, how to handle algebraic fractions, exponents, roots, and radicals, and linear and fractional equations. The topics like functions and graphs, quadratic equations, inequalities, ratio, proportion, and variation are thoroughly explained. The techniques and methodologies featured in this book are used as tools for dealing with various problems of engineering, biology, chemistry, physical sciences, psychology, sociology, and business administration. To give better practical knowledge and relatable content to the readers many real-life examples and applications of algebra are included in this text. The book will be beneficial for the students and professionals of engineering and sciences.

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7. “Algebra I Workbook For Dummies” by Mary Jane Sterling

“Algebra I Workbook For Dummies” Book Review: The book will act as a guide for the students dealing with algebra. The chapters of this book contain a thorough review of topics like fractions, exponents, factoring, linear and quadratic equations, inequalities, and graphs. The concepts and formulas featured in this textbook are efficiently explained. The given topics and methodologies are compact, precise, and elaborated in proper steps. The book consists of numerous practice problems. The book is enriched with several exercises and their explanations, hence enabling the readers in developing much needed algebraic skills.

8. “Basic Algebra II” by Nathan Jacobson

“Basic Algebra II” Book Review: The book is an excellent blend of theoretical as well as the conceptual aspects of algebra. The topics like categories, universal algebra, modules, basic structure theory of rings, classical representation theory of finite groups, elements of homological algebra, commutative ideal theory, and formally real fields are discussed in detail. The chapters of this book reflect in-depth information of the featured topics and concepts along with their proofs. The book also highlights the applications of categories and functors. Several exercises are included in this book for self-study as self-assessment of the readers. The book will be a valuable resource for the first-year graduate course in algebra.

9. “Basic Algebra” by Richard G Brown and Geraldine D Smith

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“Basic Algebra” Book Review: The book aims at presenting the fundamental principles and key concepts of algebra. The chapters of this book are straightforward, comprehensive, and reader-friendly. This book lays an emphasis on the technique of problem-solving. The topics and concepts featured in this book are described in detail and clearly explained with the help of suitable examples. For better understanding and practice of the readers, several problems are included in this book. The book will be an ideal reference for the beginners of algebra.

10. “Basic Math and Pre-Algebra Workbook For Dummies” by Mark Zegarelli

“Basic Math and Pre-Algebra Workbook For Dummies” Book Review: The book enables readers in reviewing and revising their general mathematical skills. It begins with fundamental topics like interpreting patterns, navigating the number line, rounding numbers, and estimating answers. Moving on, the basics of addition, subtraction, multiplication, and division are highlighted. The applications of commutative, associative, and distributive properties are mentioned. The chapters cover negative numbers, units, inequalities, exponents, square roots, and absolute value, along with their proper uses. A section of this book is devoted to statistics and sets. The book helps its readers in developing and enhancing their problem solving skills.


2. Algebra

1. “Topics in Algebra” by I N Herstein
2. “Algebra” by Vivek Sahai and Vikas Bist

“Algebra” Book Review: This book discusses a concise and comprehensive introduction to the basics of linear algebra. Different topics such as vector space, subspace, basis and dimension are included. A series of activities of various difficulty levels is also included in the book. This book will be useful for graduates, mathematicians and professionals.

3. “Fundamentals of Abstract Algebra” by D S Malik
4. “HIGHER ALGEBRA” by Hall and Knight

“HIGHER ALGEBRA” Book Review: This book discusses proportion, proportion, variation, arithmetic progression, geometrical progression, and progression-related harmonic progression theorems. Notation scales, surds and imaginary quantities, the principle of quadratic equations and miscellaneous equations are also explained.

5. “Algebra” by Artin

“Algebra” Book Review: This book discusses a concise and comprehensive introduction to the basics of linear algebra. Different topics such as vector space, subspace, basis and dimension are included. A series of activities of various difficulty levels is also included in the book. This book will be useful for graduates, mathematicians and professionals.

6. “Algebra For Beginners” by Hall and Knight

“Algebra For Beginners” Book Review: This book provides a full course in abstract algebra. Full facts and major theorems are used as exercises. The book also provides several thoroughly thought out examples and a selection of practice and challenge concerns. This book will be useful for graduates, mathematicians and professionals.

7. “Contemporary Abstract Algebra” by Joseph A Gallian
8. “Algebra (Step-By-Step Maths)” by V Petris Joannou

“Algebra (Step-By-Step Maths)” Book Review: This book discusses a concise and comprehensive introduction to the basics of linear algebra. Different topics such as vector space, subspace, basis and dimension are included. A series of activities of various difficulty levels is also included in the book. This book will be useful for graduates, mathematicians and professionals.

9. “Algebra: A Complete Introduction: Teach Yourself” by Hugh Neill


3. Abstract Algebra

1. “Contemporary Abstract Algebra” by Joseph A Gallian

“Contemporary Abstract Algebra”Whereas many partial solutions and sketches for the odd-numbered exercises appear in the book, the Student Solutions Manual, written by the author, has comprehensive solutions for all odd-numbered exercises and large number of even-numbered exercises. This Manual also offers many alternative solutions to those appearing in the text. These will provide the student with a better understanding of the material. This is the only available student solutions manual prepared by the author of Contemporary Abstract Algebra, Tenth Edition and is designed to supplement that text”.

2. “Abstract Algebra” by David S Dummit

“Abstract Algebra” Book Review: Abstract Algebra, 4th Edition is designed to give the reader insight into the power and beauty that accrues from a rich interplay between different areas of mathematics. The book carefully develops the theory of different algebraic structures, beginning from basic definitions to some in-depth results, using numerous examples and exercises to aid the reader’s understanding. In this way, readers gain an appreciation for how mathematical structures and their interplay lead to powerful results and insights in a number of different settings.

3. “Basic Abstract Algebra” by Bhattacharya

“Basic Abstract Algebra” Book Review: This book represents a complete course in abstract algebra, providing instructors with flexibility in the selection of topics to be taught in individual classes. All the topics presented are discussed in a direct and detailed manner. Throughout the text, complete proofs have been given for all theorems without glossing over significant details or leaving important theorems as exercises. The book contains many examples fully worked out and a variety of problems for practice and challenge. Solutions to the odd-numbered problems are provided at the end of the book. This new edition contains an introduction to lattices, a new chapter on tensor products and a discussion of the new (1993) approach to the celebrated Lasker Noether theorem. In addition, there are over 100 new problems and examples, particularly aimed at relating abstract concepts to concrete situations. Full facts and major theorems are used as exercises. The book also provides several thoroughly thought out examples and a selection of practice and challenge concerns. This book will be useful for graduates, mathematicians and professionals.

4. “Topics in Abstract Algebra” by Parthasarathi M

“Topics in Abstract Algebra” Book Review: This book is designed in accordance with the new UGC syllabus for all Indian universities at the undergraduate and advanced honours levels as well as for the first year post-graduate students of many Indian universities. Students appearing for the NET, GATE, SLET or MCA examination will find this book useful too. Moreover, the curriculum requirements of Abstract Algebra offered in engineering courses are also covered in this book. This edition has a complete chapter with worked out examples and exercises on Boolean Algebra. The Chinese remainder theorem and Euler’s Phi function has also been discussed in the appendix. Among the salient features of the book are: A rich collection of numerous examples. Visual illustrations wherever necessary. Explanatory notes in the form of footnotes. Some mind-boggling, relevant problems with their latest developments, in the Appendices. Various references to relevant web sites. Glimpses of relevant history of mathematics and mathematicians. Large number of solved exercises. Well-planned and graded exercises with objective and multiple choice questions. Answers (with hints) to large numbers of exercises.

5. “A Course In Abstract Algebra” by V K Khanna

“A Course In Abstract Algebra” Book Review: This book is designed in accordance with the new UGC syllabus for all Indian universities at the undergraduate and advanced honours levels as well as for the first year post-graduate students of many Indian universities. Students appearing for the NET, GATE, SLET or MCA examination will find this book useful too. Moreover, the curriculum requirements of Abstract Algebra offered in engineering courses are also covered in this book. This edition has a complete chapter with worked out examples and exercises on Boolean Algebra. The Chinese remainder theorem and Euler?s Phi function have also been discussed in the appendix. Among the salient features of the book are A rich collection of numerous examples Visual illustrations wherever necessary Explanatory notes in the form of footnotes Some mind-boggling, relevant problems with their latest developments, in the Appendices Various references to relevant websites Glimpses of relevant history of mathematics and mathematicians Large number of solved exercises Well-planned and graded exercises with objective and multiple choice questions Answers (with hints) to large number of exercises.

6. “Algebra: Abstract and Modern” by Swamy and Murthy

“Algebra: Abstract and Modern” Book Review: Spread across 16 chapters, this book introduces the readers to the preliminaries of algebra and then explains topics like group theory and field theory in depth. It also features a blend of numerous challenging exercises and examples that further enhance each chapter. Covering all the necessary topics on the subject, this text is an ideal text book for an undergraduate course on mathematics.

7. “Schaum’s Outline of Modern Abstract Algebra” by Frank Ayres

“Schaum’s Outline of Modern Abstract Algebra” Book Review: This powerful study tool on abstract algebra takes you step-by-step through the subject and gives you sample problems with fully worked solutions, including proofs of all important theorems. You also get additional practice problems to solve on your own, working at your own speed. In addition, this superb study guide gives you chapters on sets, integers, groups, polynomials, and vector spaces.This Schaum’s Outline gives you Practice problems with full explanations that reinforce knowledge Coverage of the most up-to-date developments in your course field In-depth review of practices and applications. Fully compatible with your classroom text, Schaum’s highlights all the important facts you need to know. Use Schaum’s to shorten your study time-and get your best test scores!

8. “Topics in Algebra” by I N Herstein

“Topics in Algebra” Book Review: This book on algebra includes extensive revisions of the material on finite groups and Galois Theory. Furthermore the book also contains new problems relating to Algebra.

9. “A First Course in Abstract Algebra” by Fraleigh
10. “Abstract Algebra” by Dipak Chatterjee

“Abstract Algebra” Book Review: This book is for undergraduate courses, this third edition has new chapters on Galois Theory and Module Theory, new solved problems and additional exercises in the chapters on group theory, boolean algebra and matrix theory.The text offers a systematic, well-planned, and elegant treatment of the main themes in abstract algebra. It begins with the fundamentals of set theory, basic algebraic structures such as groups and rings, and special classes of rings and domains, and then progresses to extension theory, vector space theory and finally matrix theory. The boolean algebra by virtue of its relation to abstract algebra also finds a proper place in the development of the text.The students develop an understanding of all the essential results such as the Cayley’s theorem, the Lagrange’s theorem, and the Isomorphism theorem, in a rigorous and precise manner.Sufficient numbers of examples have been worked out in each chapter so that the students can grasp the concepts, the ideas, and the results of structure of algebraic objects in a comprehensive way. The chapter-end exercises are designed to enhance the student’s ability to further explore and interconnect various essential notions.Besides undergraduate students of mathematics, this text is equally useful for the postgraduate students of mathematics.

11. “Computer Algebra Recipes: An Advanced Guide to Scientific Modeling” by Richard H Enns

“Computer Algebra Recipes: An Advanced Guide to Scientific Modeling” Book Review: This book aims at providing advanced guidance to scientific modelling using computer techniques. It is designed focusing on students, teachers, and professionals in the field of scientific modelling. It explains different mathematical equations to solving complex problems and how computer aided techniques can help simplify them. It expects the reader to have basic knowledge of algebra and scientific modelling. It contains mathematical and theoretical explanation along with numerous diagrams and graphs to enhance understanding. This book provides numerous solved and unsolved examples and detailed explanations.


4. Commutative Algebra

1. “Commutative Algebra” by D Eisenbud

“Commutative Algebra” Book Review: This book is understood by the knowledge of geometric concepts that played a major role in exploring algebraic geometry. It elaborates every concept from basic to advanced. It covers topics such as localization and primary decomposition through dimension theory, differentials. It also describes the various homological methods, free resolution and duality, and their connection with algebraic mathematics. The book has many exercises as well as extended chapter-end exercises which help to clear theory concepts in-depth. Another feature of the book is a chapter designed for a quick but complete treatment of Grobner’s teaching and constructivist approaches to commutative algebra and algebraic geometry flowing from it. This book will help students from beginner to advanced level of commutative algebra or algebraic geometry. It also included the applications of theory and suggestion projects for computer algebra to gain more knowledge about concepts.

2. “Commutative Ring Theory” by H Matsumura

“Commutative Ring Theory” Book Review: This book is important as the basis of algebraic geometry and complex geometry. The book is very interesting and profound on every topic in its own manner. It covers the basic material including dimension theory. It also describes different types of rings such as Cohen-Macaulay rings, Gorenstein rings, Krull rings, and valuation rings. The book also elaborates on advanced topics such as Ratliff’s theorems in the chains of the primary goal. The book is actually self-contained, but the knowledge of modern algebra is necessary at the beginner level. The book has provided chapter-end exercises for each section and tips to some of them are given at the end of the book.

3. “Cohen-Macaulay Rings” by W Bruns and J Herzog

“Cohen-Macaulay Rings” Book Review: This book elaborates the important topics of commutative algebra. It is a self-contained book. It covers the introduction to the homological and combination aspects of the theory of Cohen-Macaulay rings, Gorenstein rings. It describes a separate chapter of Hilbert functions including Macaulay’s theorem and numerical invariants derived from them. The general theory is applied to Stanley-Reisner rings, semigroup rings, determinantal rings, and rings of invariants. The final chapters are given by Hochster’s view of the great Cohen-Macaulay modules and their application, including the Pasnean-Szpiro crazy theorem. The book provides many solved examples as well as exercises to gain more knowledge about the concept. This book is very useful for the graduate courses in algebra. As the only modern, broad account of the subject it will be essential reading for researchers in commutative algebra.

4. “Introduction To Commutative Algebra” by Michael Atiyah

“Introduction To Commutative Algebra” Book Review: This book is designed mainly for the third-year undergraduates of Oxford University. The main goal of this book is to give proper introduction to the subject Commutative Algebra. It is designed to be read by students who have a first elementary course in general algebra. On the other hand, it is not intended as a substitute for the more voluminous tracts such as Zariski-Samuel or Bourbaki. The book concentrated on certain central topics, and large areas, such as field theory. In theoretical concept, this book covers more basics than Northcott and the content is also different and more clear. It follows the modern trend and gives more focus on each module and localization.

5. “Introduction To Commutative Algebra” by Michael Atiyah
6. “Commutative Algebra: An Introduction” by William Hoffman and Xiaohong Jia

“Commutative Algebra: An Introduction” Book Review: The main purpose of this book is to present basic ideas in cumulative algebra and algebraic geometry. It presents interesting topics of research focused mainly on the themes of Grobner bases, resultants and syzygies. The aim of this book is to give supplementary books to the reader towards future research in the field of algebraic geometry. The book provides a perfect combination of definitions and proofs with examples. It also elaborates the use of different software such as Mathematica and Singular. The book gives a perfect balance of theory and its applications with separate parts to understand the concept more clearly. Part of the application of this chapter is suitable for the reader who knows the algebra of small fluctuations and algebraic geometry, and serves as a guide for some interesting research topics. What is new about this book is that the content presented here is a unique combination of the most important methods and results of current research. The aim is to equip students with basic algebraic and geometric tools, to gain their research interests, and to initiate specific research projects in related areas.

7. “The Geometry of Syzygies: A Second Course in Algebraic Geometry and Commutative Algebra” by David Eisenbud

“The Geometry of Syzygies: A Second Course in Algebraic Geometry and Commutative Algebra” Book Review: This book consists of basic examples and techniques in the area of algebraic geometry and commutative algebra. It demonstrates the use of syzygies in many geometric concepts, from compilation to the study of canonical curves. The text has served as the basis for graduate studies by the author in Berkeley, Brandeis and Paris. It is also easy to read for yourself by a student who knows a little algebra alternating algebra and geometry. As an aid to the reader, the appendix provides a summary of flexible algebra, combining examples and major results from a variety of topics.

8. “A Course in Commutative Algebra” by Gregor Kemper

“A Course in Commutative Algebra” Book Review: This book gives the modern introduction into commutative algebra. It mainly serves as a textbook guide for a course of one or two semesters, or for self study. It is written in a simple and student-friendly manner. The carefully chosen subject matter focuses more on the concepts and results at the center of the field. The book maintains an ongoing view of the geometric environment. It enables the reader to gain a deeper understanding of the subject. Although it elaborates theory, three chapters are designed for computational aspects. The book has lots of examples and exercises that enrich the concept.

9. “Commutative Algebra” by N S Gopalakrishnan
10. “An Introductory Course in Commutative Algebra” by A W Chatters and C R Hajarnavis

“An Introductory Course in Commutative Algebra” Book Review: This book gives a concise introduction to topics in commutative algebra, with an importance of practical examples and applications. It combines good algebraic theory with applications to number theory. It also elaborates problems in classical greek geometry, and the theory of finite fields which has important uses in other branches of science. The book covers important topics such as rings and euclidean rings, the four-squares theorem, fields and field extensions, finite cyclic groups and finite fields. The content of the book prepares the way for the future learning of abstract algebra, but it could also form the basis of an entire course.


5. Introduction to Algebraic Geometry

1. “Algebraic Geometry for Scientists and Engineers” by S S Abhyankar

“Algebraic Geometry for Scientists and Engineers” Book Review: The book will be a valuable source for the graduate students and advanced undergraduates in mathematics. It will be equally important for the engineers and scientists mainly involved in computer science. The chapters of this book present various concepts of modern algebraic geometry as well as algebraic curves and surfaces. The topics like rational and polynomial parameterization, functions and differentials on a curve, branches and valuations, and resolution of singularities are thoroughly explained. The book highlights applications and involvement of algebraic geometry in different areas of science and industry.

2. “Algebraic Curves” by W Fulton
3. “Undergraduate Algebraic Geometry” by M Reid

“Undergraduate Algebraic Geometry” Book Review: The book aims at presenting a reader-friendly introduction of algebraic geometry. The chapters of this book present the fundamental concepts of algebraic geometry namely, plane conics, cubics and the group law, affine and projective varieties, and non-singularity and dimension. The book highlights the relationship of algebraic geometry with commutative algebra, topology, differential geometry, and number theory. The content of this book is supported by several examples and exercises. The book will be suitable for all the undergraduate mathematicians.

4. “Basic Algebraic Geometry” by I R Shafarevich
5. “Introduction to Algebraic Geometry” by Justin R Smith

“Introduction to Algebraic Geometry” Book Review: The book is a well-structured and self-contained piece of writing, providing a strong base in linear algebra. The chapters of this book cover all the major topics related to classical result, affine varieties, varieties and schemes, projective varieties, and curves. Point-set topology is thoroughly explained. The final section of the book consists of the appendices on algebra, commutative algebra, sheaf-theory and cohomology. To give better practical knowledge and relatable content to the readers, the applications of algebraic geometry in robotics and other fields are mentioned. The book will be beneficial for the graduate and advanced undergraduate students of mathematics.

6. “Introduction to Algebraic Geometry” by Serge Lang

“Introduction to Algebraic Geometry” Book Review: The book presents basic concepts, principles, and major aspects of Weil-Zariski algebraic geometry. The initial chapters of this book are based on theory of places, algebraic varieties, absolute theory of varieties, product, projections, and correspondence, and normal varieties. The remaining chapters cover divisors and linear systems, differential forms, theory of simple points, algebraic groups, and Riemann-Roch theorem. The book also introduces Weil’s Foundations along with latest topics and recent advances in algebraic geometry.

7. “Introduction to Algebraic Geometry” by Brendan Hassett

“Introduction to Algebraic Geometry” Book Review: This book focuses on presenting a fair introduction to the major concepts of algebraic geometry. The applications of algebraic geometry in various fields namely, engineering, computer science, statistics, and computational biology are mentioned in this book. The techniques and concepts essential computation and many other modern processes are featured in this text. The content of this book is illustrated with several examples and algorithms. The book will be useful for the advanced undergraduate and graduate students of mathematics as well as the researchers in application areas.

8. “Introduction to Algebraic Geometry” by W Gordon Welchman

“Introduction to Algebraic Geometry” Book Review: The book is a well-structured and comprehensive presentation of projective geometry along with the similar topic in space of more than two dimensions. It starts with an analysis and basic principles of geometry, and hence establishes a strong base for advanced topics. Moving further, the theory of conics, metrical geometry, applications of matrix algebra, and invariants and covariants are discussed in detail. The applications of featured techniques in various fields and subjects are highlighted. The book will be an ideal resource for the students and professionals of mathematics as well as individuals interested in the history of education.

9. “An Introduction to Manifolds” by Loring W Tu

“An Introduction to Manifolds” Book Review: The book aims at presenting a fundamental theory of manifolds along with the key concepts, basic principles, and major topics. The chapters of this book revolve around several concepts of algebra, topology, and analysis, manifolds. The applications of featured concepts and theories in classical mechanics, general relativity, and quantum field theory are clearly illustrated. The book enables its readers in performing computation in simple spaces. For better understanding of the readers, chapters contain several problems and exercises along with hints for their solutions. The book will be suitable for the students pursuing their graduation in mathematics.

10. “Introduction to algebraic geometry” by J G Semple

“Introduction to algebraic geometry” Book Review: The book reflects an overview of geometrical aspects of algebraic equations. The chapters of this book are fully updated and present modern fundamental techniques, latest topics, and recent amendments in the field of algebraic geometry. The impact and applications of algebraic geometry in various areas like plane curves, quadratic transformations, the geometry of line systems, and the projective characters of curves and surfaces are highlighted in this book. The individuals seeking for deep knowledge in the field of algebraic geometry will find this text helpful.


6. Algebraic Topology

1. “Introduction to Functional Analysis” by A Taylor and D Lay

“Introduction to Functional Analysis” Book Review: The book is a well-structured and self-contained piece of writing featuring the theory of normed linear spaces and of linear mappings. It aims in providing the essential base for further study in many areas of analysis. The chapters based on Banach algebras, material on weak topologies and duality, equicontinuity, Krein-Milman theorem, and theory of Fredholm operators are included in this book. The book also highlights the problems faced in linear algebra, classical analysis, and differential and integral equations.

2. “Collectively Compact Operator Approximation Theory” by P M Anselone
3. “Introduction to Functional Analysis” by A H Siddiqi

“Introduction to Functional Analysis” Book Review: The book aims at presenting the major aspects and important topics of functional analysis. The chapters of this book reflect basic theorems dealing with properties of functional and operators namely, Hahn-Banach theorem, Banach-Steinhaus theorem, Open mapping theorem and Closed graph theorem. The book also highlights the applications of functional analysis in operator equations, boundary value problems, optimization, variational inequalities, finite element methods, optimal control, and wavelets. The students and professionals seeking deep information in functional analysis will find this text helpful.

4. “Algebraic Topology” by Allen Hatcher

“Algebraic Topology” Book Review: The book delicately focuses students, researchers, professionals, engineers in the development of algebraic topology. All the basic concepts of algebraic topology are covered in this text, hence making it an ideal choice for self-study. The chapters of this book cover all the major topics of fundamental group and covering spaces, homology and cohomology, higher homotopy groups, and homotopy theory. The content of this book is supported with many examples and exercises. This book will be useful for students and teachers.

5. “Algebraic Topology: A First Course” by William Fulton

“Algebraic Topology: A First Course” Book Review: The book presents important concepts and topics of algebraic topology along with their applications in various areas of mathematics. The chapters of this book describe topics like relation between homology and integration, plane domains, Riemann surfaces, winding numbers, degrees of mappings, and fixed-point theorems. Various applications of algebraic topology namely, Jordan curve theorem and invariance of domain are included in this text. The book will be beneficial for the students of mathematics and science.

6. “Algebraic Topology” by C R F Maunder

“Algebraic Topology” Book Review: The book aims at presenting basic algebraic topology from a homotopy theoretical point-of-view. The chapters of this book feature construction homology or homotopy groups of a topological space, homotopy theory, CW-complexes, and co-homology groups associated with a general Ω-spectrum. The applications of algebraic topology to various topological problems such as classification of surfaces and duality theorems for manifolds are highlighted in this book. For better understanding of the readers many examples and exercises are included in this text. The book will be valuable for the undergraduate and first-year graduate students of related to homotopy or homology theory.

7. “Algebraic Topology” by Robert M Switzer

“Algebraic Topology” Book Review: The book is a contemporary piece of writing presenting the latest topics and untouched aspects of homotopy and homology. The chapters of this book are comprehensive, precise, and revolve around homotopy groups of sphere and computation of various cobordism groups. The stable homotopy theory is featured in this book along with its basic concepts, principle methods, and applications in different fields. The book will be a good resource for the professionals and experts in the field of algebraic topology.

8. “A Concise Course in Algebraic Topology” by J P May

“A Concise Course in Algebraic Topology” Book Review: The book will be suitable for the teachers and advanced graduate students of mathematics. The chapters of this book are well-structured, self-contained, and deliver deep information on various topics of algebraic topology. The later section of the book portrays the sketches of substantial areas of algebraic topology. The applications of algebraic topology in various advanced fields namely geometry, topology, differential geometry, algebraic geometry and lie groups are highlighted in this piece of writing. The book consists of numerous problems for self-study and self-assessment of the readers.

9. “Basic Algebraic Topology” by Anant R Shastri

“Basic Algebraic Topology” Book Review: The book reflects deep information on real analysis, point-set topology, and basic algebra. It is broadly classified into three sections featuring introduction of algebraic topology, cell complexes and simplicial complexes, and covering spaces and fundamental groups, respectively. The Poincaré duality, De Rham theorem, cohomology of sheaves, Čech cohomology is discussed in detail. The topics like higher homotopy groups, Hurewicz’s isomorphism theorem, obstruction theory, Eilenberg-MacLane spaces, and Moore-Postnikov decomposition are thoroughly explained. The content of this book is enriched with several exercises and applications of algebraic topology. The book will be appropriate for the graduate students, researchers, and working mathematicians related to the field of algebraic topology.

10. “Elements of Algebraic Topology” by James R Munkres

“Elements of Algebraic Topology” Book Review: The book aims in providing readers a strong foundation in the field of algebraic topology. The chapters of this book are reader-friendly, self-contained, and contain a detailed description of homology and cohomology theory, universal coefficient theorems, Kunneth theorem, and duality in manifolds. The applications of algebraic topology in the classical theorems of point-set topology are clearly mentioned in this book. The book will be a great source of information for the beginners in algebraic topology, as it explains the complex and advanced topics, quite efficiently.


7. Linear Algebra

1. “Elementary Linear Algebra with Applications” by H Anton

“Elementary Linear Algebra with Applications” Book Review: Elementary Linear Algebra, gives an elementary treatment of linear algebra that is suitable for students in their freshman or sophomore year. The purpose is to present the fundamentals of linear algebra in the clearest possible way. A simple explanation is the main consideration. Calculus is a prerequisite along with there are clearly labeled exercises and examples for students who are studying calculus. Those exercises can help you strengthen your skills. There is no need for technology, if someone would like to use calculators with linear algebra capabilities, exercises have been included at the ends of the chapters that allow for further exploration of chapter’s contents.

2. “Linear Algebra and its Applications” by G Strang

“Linear Algebra and its Applications” Book Review: This book is written in a student-friendly style and teaches real Mathematics. The student will experience a gear shift while going through it especially from the Introduction of Vector Spaces. Throughout the book, the theory is well presented, allowing students to have a deep dive from pure mathematics to applied mathematics. The exercises in the book are well designed and have many new problems added to it along with Singular Value Decomposition. Here a student can learn how the algorithm fits linear Algebra with an introduction to complex numbers. This book is a bonus for Computer Science students.

3. “Linear Algebra – A Geometric Approach” by S Kumaresan

“Linear Algebra – A Geometric Approach” Book Review: This book is highly readable, clear, and concise on Linear Algebra and is for undergraduate courses in mathematics. The key focus is on analytical geometry explanations to make a clear view of the topic. From the beginning, the topic is presented as simultaneous linear equations and their geometric interpretation which is the theme of the subject. Abstract algebraic concepts with geometric notions are a distinguishing feature of this book. It is designed such as to help students in Multivariable calculus and differential geometry. The explanation and concepts are well presented here.

4. “Advanced Engineering Mathematics” by E Kreyszig

“Advanced Engineering Mathematics” Book Review: This book is well designed to let you taste the real cream of engineering mathematics and is also popular among Engineering students. This book is also a textbook of mathematics in various Engineering colleges as the problems in the books are so well designed that it will let you revise all your basic concepts in mathematics. This book is thoroughly updated and is streamlined to reflect the upliftment in the field. It covers all the advanced topics of engineering mathematics like Linear Algebra, Vector Calculus, Partial Differential Equation, Optimisation, Graphs, Complex Analysis, Statics & Probability so that students can relate to practical problems and can grasp their best.

5. “Introduction to Linear Algebra” by Gilbert Strang

“Introduction to Linear Algebra” Book Review: This book is well described and simple to Linear Algebra and has many breakthroughs within the subjects itself. This is an easy to read textbook that incorporates all the topics essential for detailed knowledge of the subject .The book teaches theory behind everything so it’s much engaging with the subject.The textbook includes many challenging problems for better grip on the topic .The book has been divided into seven different topics such as differential calculus, graph theory, statics, Fourier transformation methods, LPP and computer graphics and is complete for a deep overview of the subject.

6. “Linear Algebra: Step by Step” by Kuldeep Singh

“Linear Algebra: Step by Step” Book Review: This book has a large number of examples and their step-by-step explanation for each topic. The topic is simplified in a way that allows distance learning with a concise solution to the set of problems freely available. This book consists of miscellaneous exercises at the end of each chapter which covers questions from past papers and also from various university exams helping the reader to boost his or her confidence. It also has short historical biographies of the leading players of Linear Algebra.This book is dynamic and has engaging style which includes question answer tests for the reader to make a clear view of the methods rather than rote learning. It also has exclusive interviews with the professionals who use the topic in their real life.

7. “Linear Algebra and Its Applications” by David C Lay and Steven R Lay

“Linear Algebra and Its Applications” Book Review: In this book, the traditional Linear Algebra texts are relatively easy to understand for students as the topic here is presented here in a familiar manner and with a concrete setting. Students often face problems with abstract topics like linear independence, spanning, subspace, vector space, transformations, and the book takes good care of this as the topic needs time to assimilate. These topics are important and understanding the topics is vital and this book makes it more accessible by its simple and explanatory demonstration which is easy to understand for students.

8. “Linear Algebra” by Georgi E Shilov

“Linear Algebra” Book Review: In this book, the course has been made more accessible and useful. This book goes from the elementary level and easily catches up with advanced topics along with covering all the standard topics of an undergraduate or a beginning graduate course. The material here is demonstrated here in a simple style. Here the problems are included and their answers at the back. This book is good for students who want to learn techniques as it has an abundance of problems and examples so as to give the reader a good experience of applicability if the topic and is also useful for self-study and the classroom as well.

9. “Linear Algebra For Dummies” by Mary Jane Sterling

“Linear Algebra For Dummies” Book Review: This book is an easy to follow guide for the topic which offers a clear view of real-world application of Linear Algebra in many areas like programming, Engineering. This book is near a college-level linear algebra course, In which students study the basic operations and then abstract topics like vector space, linear transformation, determinants, and eigenvalues & vectors. This book gives students both theoretical and practical ways to solve different types of problems. The book presents the information in such a way that the reader can not only know how to solve it but also why to solve it.

10. “Linear Algebra Done Right” by Sheldon Axler

“Linear Algebra Done Right” Book Review: This book for linear algebra is aimed at both graduate and undergraduate students. The narrative approach of this book to the topic focuses on the central goal of the topic so that students can understand the linear operations on finite-dimensional vector spaces. The book then deals with topics like linear maps, eigenvalues, and eigenvectors. Inner-product spaces, leading to the finite-dimensional spectral theorem and its consequences. In this book the concepts are concise and proofs are simple with a variety of interesting exercises on each chapter to help students in understanding the topic well and manipulate the objects of linear algebra. This book comes with many updated examples to illustrate the key ideas of linear algebra which include product spaces, quotient spaces, and dual spaces. There is no prerequisite for this book except mathematical maturity.

11. “A Concise Introduction to Linear Algebra” by Geza Schay G Za Schay Schay

“A Concise Introduction to Linear Algebra” Book Review: This book provides a detailed overview on introduction to linear algebra. It focuses on the mathematical fundamentals, investigates several interesting applications, including a section on computer graphics. It contains a chapter on numerical methods, and many exercises and examples using MATLAB. Several real-world problems are stated, and detailed solutions provided along with theoretical and mathematical explanation. The book is designed focusing on students and teachers in the various fields of engineering and science.

12. “Introduction to Linear Algebra” by Lang

“Introduction to Linear Algebra” Book Review: This book provides a detailed overview on introduction to linear algebra. It discusses the relation between the geometry and the algebra underlying the subject. It provides concrete examples of the notions in linear algebra. It contains discussion of linear equations, matrices, and Gaussian elimination. It also talks about vector spaces, linear maps, scalar products, determinants, and eigenvalues. The book contains many exercises which help enhance understanding of the reader. The book is designed focusing on students and teachers in the various fields of engineering and science.

13. “Introduction to Linear Algebra” by Inder K Rana

“Introduction to Linear Algebra” Book Review: This book provides a fundamental overview on introduction to linear algebra. It talks about the Euclidean space, systems of linear equations, linear independence and dependence, determinants, vector spaces, and much more. It also discusses linear transformations, inner product spaces, orthogonal projections and orthogonal basis, isometries, and orthogonal matrices and much more. It contains numerous solved and unsolved examples to enhance understanding of the reader. The book is designed focusing on students and teachers in the various fields of engineering and science.


8. Applied Linear Algebra

1. “Linear Algebra” by K Hoffman and R Kunze

Book Review: The book introduces the basic and advanced concepts of linear algebra. It contains intuitive introductions along with examples that expose important ideas to the users and also demonstrate the usage of various theorem results. The book also contains chapters on linear equations, vector spaces, linear transformations, polynomials, determinants, elementary canonical forms, rational forms, Jordan forms, inner product spaces and its operators and bilinear forms. This book is an excellent book for all the readers interested in linear algebra.

2. “Matrix Computations” by G H Golub and C F Van Loan

Book Review: This book is a very good text book for computer science which contains very useful information covering the mathematical background and algorithmic skills which are used in the production of numerical software. The book contains revised chapters on matrix multiplication problems, parallel matrix computations, CS decomposition treatment, floating point arithmetic operations, gram-schmidt process, concepts of GMRES, QMR and other methods which demonstrate the sparse unsymmetric linear system problems.

3. “Functional Analysis” by G Bachman and L Narici

Book Review: The book contains information about basic and advanced concepts of linear algebra, advanced calculus, engineering and physics. The book contains chapters on inner product spaces, normed spaces, metric spaces, topological spaces, orthonormal sets, Hahn-banach theorem, consequences and results of various theorems, spectral notions, square roots, spectral decomposition theorem and many other topics. Every chapter contains exercises which tests the reader’s understanding. The book also contains glossary of definitions, proof of theorems which benefits the readers.

4. “Introductory Functional Analysis with Applications” by Erwin Kreyszig

Book Review: The book contains information on introduction to functional analysis along with various applications. The book provides avenues for the application of functional analysis as well as practical study of mathematics and natural sciences. The book also contains worked examples on Hilbert space theory, banach spaces thereby stressing on the concepts, principles, methods and major applications of functional analysis. The book is concerned with the study of spaces of functions. The book also provides information about differential and integral equations, calculus of variations and quantum mechanics.

5. “Applied Linear Algebra and Optimization Using MATLAB” by Rizwan Butt

“Applied Linear Algebra and Optimization using MATLAB” Book Review: This book supplies numerous m-files, applications, and practical examples to solve problems on linear algebra and optimization. Short programs in MATLAB are provided to solve problems associated with systems of linear equations, matrices, vectors, computer graphics, etc. A CD-ROM with all of the figures, m-files for all of the programs, and MATLAB simulations from industry is also provided with this book. The book successfully balances the theoretical principles with the applications, keeping in mind the need for computational speed and accuracy. This book is intended for computer scientists, engineers, physicists or students in computational courses.

6. “APPLIED LINEAR ALGEBRA AND MATRIX ANALYSIS” by Thomas S Shores

“Applied Linear Algebra and Matrix Analysis” Book Review: This book seamlessly integrates the theoretical, computational, and practical aspects of matrix and linear algebra while also emphasizing their interdependence. Here, linear algebra is treated as an experimental science with the help of examples, computer exercises, and projects. No specific hardware or software platforms have been used in this book. A set of exercises are also provided at the end of each chapter. This book is intended for a one-semester course for engineering and science students.

7. “HANDBOOK OF APPLIED LINEAR ALGEBRA” by SYLVESTER MURRAY
8. “Linear Algebra: Pure & Applied” by Edgar G Goodaire

“Linear Algebra: Pure & Applied” Book Review: This book provides a comprehensive coverage of the fundamental definitions and theorems of linear algebra, pseudoinverse and singular value decomposition using a matrix-oriented approach. Linear combination, linear independence and span are introduced after geometry of Euclidean 3-space. Vector spaces are covered up to Euclidean n-space and linear transformations to matrices. Markov chains, electric circuits, facial recognition, computer graphics, quadratic forms and conic sections are some of the applications of linear algebra that are covered. Coding theory and least squares with special focus on the system Ax=b, make the book ideal for students as well as researchers and professionals.

9. “Linear Algebra over Commutative Rings” by Mcdonald

“Linear Algebra over Commutative Rings” Book Review: This book consists of lecture notes on the topic of linear algebra over commutative rings from the University of Oklahoma. An introduction of matrix theory over commutative rings is followed by the analysis of structure theory of a projective module. This book is suitable for students, researchers, and professors.

10. “THEOREMS AND APPLIED PRINCIPLES IN LINEAR ALGEBRA” by Prof. Febe Czetyrbok

“Theorems and Applied Principles in Linear Algebra” Book Review: This book extensively covers the various theorems and principles of linear algebra along with its physical applications in the real world. Population growth, stability analysis, signal processing, normal modes of oscillations, waves, Markov chains, and electrostatics are some of the applications of linear algebra that are covered in this book. Students and professionals can refer to this book.


9. Linear, Matrix, Banach, Commutative, Lie Groups and Lie Algebra

1. “Algebra II Workbook For Dummies” by Mary Jane Sterling

“Algebra II Workbook For Dummies” Book Review: This book focuses on solving many types of Algebra II problems in a step–by–step manner. Each problem has explanations to sharpen skills and improve performance. The book covers linear and quadratic equations, polynomials, inequalities, graphs, sequences and sets. Complex numbers, matrices, algebra with step by step answers are covered in the book.

2. “Schaum’s Outline of Linear Algebra, 5th Edition: 612 Solved Problems + 25 Videos” by Seymour Lipschutz

“Schaum’s Outline of Linear Algebra, 5th Edition: 612 Solved Problems + 25 Videos” Book Review: This book includes 612 fully solved problems, examples, and practice exercises to sharpen problem-solving skills. The book features 25 detailed videos of maths instructors who explain how to solve the most commonly tested problems. Topic wise format with examples, solved problems, and practice exercises are all covered in this book.

3. “3,000 Solved Problems in Linear Algebra (Schaum’s Solved Problems Series)” by Seymour Lipschutz

“3,000 Solved Problems in Linear Algebra (Schaum’s Solved Problems Series)” Book Review: This book has 3000 solved problems with complete solutions, an index to locate the types of problems and techniques for choosing the correct approach to problems.

4. “Matrix Algebra: Exercises and Solutions” by David A Harville

“Matrix Algebra: Exercises and Solutions” Book Review: This book contains 300 exercises and solutions of topics in matrix algebra. The book includes detailed summaries of all relevant terminology and notation. The book covers topics on special interest and relevance in statistics and related disciplines. This book will act as a guide for students and researchers in matrix algebra and also to mathematicians and statisticians. The book also encourages an active environment in the learning process.

5. “Lie Groups and Lie Algebras for Physicists” by Susumu Okubo and Ashok Das

“Lie Groups and Lie Algebras for Physicists” Book Review: This book is beneficial for graduate students of theoretical physics and quantum mechanics as well as researchers interested in applications of Lie group theory and Lie algebras in physics. This book focuses on inter-relations of representation theories of Lie groups and the corresponding Lie algebras.

6. “Lie Groups Lie Algebras And Some Of Their Applications” by Robert Gilmore

“Lie Groups Lie Algebras And Some Of Their Applications” Book Review: This book helps the upper-level undergraduate students to have clear concepts regarding Lie group theory and its physical applications. This book is designed for modern physical theories. The calculations remain unchanged from one field of physics to another, altering only in terms of symbols and the language. The book introduces classical groups, continuous groups, Lie groups and Lie algebra. The book also contains root spaces and Dynkin diagrams, real forms, and contractions and expansions. Numerous exercises, solved problems, figures and illustrations are all included.

7. “Complex Semisimple Lie Algebras” by Jean-Pierre Serre and Glen Jones

“Complex Semisimple Lie Algebras” Book Review: This book provides the basic theory of semi simple Lie algebras over the complex numbers. This book covers topics on the general properties of nilpotent, solvable, cartan subalgebras, root systems, and linear representations. Connection between Lie algebras, complex groups and compact groups are all mentioned in the book.

8. “Non-commutative Gelfand Theories: A Tool-kit for Operator Theorists and Numerical Analysts (Universitext)” by Steffen Roch and Pedro A Santos

“Non-commutative Gelfand Theories: A Tool-kit for Operator Theorists and Numerical Analysts (Universitext)” Book Review: This book introduces basic concepts for the study of Banach algebras. The book contains an algebra with a so-called polynomial identity or in short Pl-algebra. The book also highlights a number of selected examples used to demonstrate how this theory can be successfully applied to problems in operator theory and numerical analysis. Non-commutative Gelfand theories, PI-algebras, Mellin techniques and limit operator techniques are mentioned in the book. It helps the readers with fundamental knowledge of analysis, functional analysis and algebra. This book is suitable to the 4th year students of mathematics or physics, to researchers in the areas of operator theory, numerical analysis, and the general theory of Banach algebras.

9. “Banach Embedding Properties of Non-Commutative $Lp$-Spaces” by Haagerup and Rosenthal

“Banach Embedding Properties of Non-Commutative $Lp$-Spaces” Book Review: This book covers thirteen isomorphism types and the corresponding embedding properties via an eight level Hasse diagram.

10. “Linear Algebraic Groups” by T A Springer

“Linear Algebraic Groups” Book Review: This book highlights the theory of linear algebraic groups over an algebraically closed field. The book also covers the theory of arbitrary fields, self-contained treatment of the prerequisites from algebraic geometry and commutative algebra, as well as basic results on reductive groups. This book acts as a guide for introductory graduate courses on linear algebraic groups.

People who are searching for Free downloads of books and free pdf copies of these books on Algebra – we would like to mention that we don’t have free downloadable pdf copies of these good books and one should look for free pdf copies from these Authors only if they have explicitly made it free to download and read them.

We have created a collection of best reference books on “Algebra” so that one can readily see the list of top books on “Algebra” and buy the books either online or offline.

If any more book needs to be added to the list of best books on Algebra subject, please let us know.

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Manish Bhojasia - Founder & CTO at Sanfoundry
Manish Bhojasia, a technology veteran with 20+ years @ Cisco & Wipro, is Founder and CTO at Sanfoundry. He lives in Bangalore, and focuses on development of Linux Kernel, SAN Technologies, Advanced C, Data Structures & Alogrithms. Stay connected with him at LinkedIn.

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