45 Best Books on Geometry

We have compiled a list of the Best Reference Books on Geometry, which are used by students of top universities, and colleges. This will help you choose the right book depending on if you are a beginner or an expert. Here is the complete list of Geometry Books with their authors, publishers, and an unbiased review of them as well as links to the Amazon website to directly purchase them. If permissible, you can also download the free PDF books on Geometry below.

1. Computational Geometry

 
1."Computational Geometry: Algorithms and Applications" by Mark de Berg
Book Review: The book initiates each chapter by presenting real-world problems that require computational geometry techniques for their solution. The provided solutions are straightforward and practical to implement. The book encompasses a variety of techniques such as divide and conquer, plane sweep, and randomized algorithms. Each chapter concludes with a set of exercises to aid the reader in comprehending the presented material. The algorithms are described using pseudo code, making them more accessible for implementation.

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2."Computational Geometry: An Introduction" by F P Preparata and Michael I Shamos
Book Review: The aim of this book is to present the fundamental concepts of computational geometry that are applicable in both computer science and mathematics fields. The book is based on a systematic study of research results obtained in the past decade. It offers a clear presentation of basic ideas, important combinatorial structures, and essential algorithmic techniques. The book is richly illustrated with numerous figures and examples to facilitate understanding. It is an excellent textbook for graduate students, researchers, and professionals working in the areas of computer-aided design, computer graphics, and robotics.

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3."Computational Geometry in C" by Joseph O Rourke
Book Review: The focus of this book is on the application of geometric algorithms in computer graphics, engineering design and robotics. The book presents various techniques in computational geometry, such as polygon triangulations, convex hulls, voronoi diagrams, geometric searching, and motion planning. It is designed to be a comprehensive reference book for practitioners and covers the necessary mathematical background. Additionally, the book includes chapters on randomized algorithms for polygon triangulation, planar point location, and intersection algorithms for ray segment, ray triangle and point polyhedron.

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4."Discrete And Computational Geometry" by Mikio Kano Jin Akiyama
“Discrete and Computational Geometry” Book Review: This book is an ideal introductory textbook for students interested in discrete geometry and its applications. The book covers a wide range of topics, from basic concepts like convexity and polyhedra, to more advanced topics such as Voronoi diagrams, Delaunay triangulations, and computational complexity. Each chapter is well-organized and includes a variety of exercises and problems for students to work through. The book also includes several applications of discrete geometry, such as computer graphics, robotics, and crystallography.

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5."Handbook of Computational Geometry" by Urrutia Sack
“Handbook of Computational Geometry” Book Review: The book presents a comprehensive introduction to essential concepts and findings in Computational Geometry. The authors have covered state-of-the-art methods and solutions to geometric problems, as well as alternative approaches to problem-solving. As this topic is directly relevant to fields such as Geographic Information Systems, Robotics, and Computer Graphics, professionals and students in these domains can benefit from this book as a reference guide.

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6."Scg 10 Proceedings of the 26th Annual Symposium on Computational Geometry" by Computational Geometry Conference
“SCG 10 Proceedings of the 26th Annual Symposium on Computational Geometry” Book Review: This book covers a wide range of topics in computational geometry presented at the Annual Symposium on Computational Geometry. It includes mathematical, numerical, and algebraic issues, as well as the design, analysis, and implementation of algorithms and data structures. The book also covers the lower bounds on computational complexity, computational topology, discrete and combinatorial geometry, and novel algorithmic applications of geometry in various fields such as computer graphics, scientific computing, and robotics. This is an essential reference for professionals and students interested in the applications of computational geometry in different areas.

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7."Advances in Robot Kinematics and Computational Geometry" by Lenarcic
“Advances in Robot Kinematics and Computational Geometry” Book Review: The book explores the latest developments in robot kinematics and computational geometry. It covers important areas of research in kinematics and computational geometry and how they are applied to robots and mechanisms. The book consists of twelve sections, covering topics such as mobile robot kinematics, control, inverse kinematics, calibration, analysis, performance, design, parallel manipulators, and motion planning. It also includes sections on computational geometry in kinematics, workspace, trajectory analysis, force analysis, and elasticity analysis. The book is a useful resource for graduate students, researchers, mathematicians, and engineers interested in the mathematical modeling, design, control, and simulation of robots and mechanisms.

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8."Protein Geometry, Classification, Topology and Symmetry: A Computational Analysis of Structure" by Andras Aszodi and William R Taylor
“Protein Geometry, Classification, Topology and Symmetry: A Computational Analysis of Structure” Book Review: The objective of this book is to uncover the underlying patterns in protein construction through an examination of their structural principles. It provides a comprehensive review of computer methods for statistical and structural analysis, including automatic comparison and classification of structures. The book also analyzes the current state of protein classification, explores knotted topologies, and discusses abstract geometric and topological representations. The book concludes with a discussion of the origin of higher-level symmetries in protein structures. This text is a suitable resource for post-graduate courses and researchers interested in the study of protein structures.

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2. Differential Geometry

 
1."Differential Geometry of Curves and Surfaces" by M doCarmo
“Differential Geometry of Curves and Surfaces” Book Review: This book presents an alternative approach to the topic of differential geometry by emphasizing basic geometrical facts over machinery and random details. The book explores the relation between differential formulas such as the Gauss integral for a link or the integral of Gaussian curvature on a surface and topological invariants like the linking number or the Euler characteristic. It covers local and global aspects of the differential geometry of curves and surfaces, with extensive use of elementary linear algebra. The book contains numerous well-written examples and problem hints, and is suitable for both undergraduate and graduate students with a brief knowledge of calculus in several variables.

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2."Elementary Differential Geometry" by B O`Neill
“Elementary Differential Geometry” Book Review: This book is an introductory guide to the geometry of curves and surfaces, with an emphasis on topological properties, geodesics, singularities of vector fields, and the theorems of Bonnet and Hadamard. It also provides an update on the commands for symbolic computation programs like Mathematica or Maple, along with additional computer exercises. The book covers a wide range of topics including Calculus on Euclidean Space, Frame Fields, Euclidean Geometry, Calculus on a Surface, Shape Operators, Geometry of Surfaces in R3, Riemannian Geometry, and Global Structures of Surfaces. It is intended for courses, introductory graduate-level courses, individual study by mathematicians, and those in applied areas like physics.

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3."Differential Geometry" by J J Stoker
“Differential Geometry” Book Review: This book offers a comprehensive introduction to the topic of differential geometry, presented in a way that is accessible to both mathematicians and non-specialists. The material is presented using three different notations: vector algebra and calculus, tensor calculus, and differential forms. The book covers a range of topics including operations with vectors, plane and space curves, surface theory, differential equations, and differential geometry of manifolds. There are also sections on relativity and applications of surface theory. Two appendices provide additional background on linear algebra and analysis. This book assumes a basic familiarity with these topics.

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4."Elementary Topics in Differential Geometry" by J A Thorpe
“Elementary Topics in Differential Geometry” Book Review: This book provides a simple and accessible introduction to linear algebra at a sophomore level, with the advantage of aiding in the understanding of differential equations and multivariate calculus. The focus is on 2-dimensional surfaces in 3-space rather than arbitrary dimensions, providing students with a solid foundation in higher dimensions. Topics covered include Graphs and Level Sets, The Tangent Space, Surfaces, The Gauss Map, Curvature of Plane Curves, Convex Surfaces, and Surface Area and Volume. This book is suitable for students who have completed their sophomore year and have a preliminary understanding of spaces of many dimensions.

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5."Differential Geometry" by Mittal
“Differential Geometry” Book Review: This book provides a comprehensive overview of the properties of curves in space and their analysis in variational calculus or calculus of variations, which deals with the maximization or minimization of functionals. The book includes a wide range of problems and exercises to enhance understanding and covers fundamental concepts such as definitions of curves in space, tangent lines to curves, osculating planes, principal normal, and binormal. It also offers numerous solved examples and exercises for further practice. The content of the book is fully updated to reflect the latest developments in the field.

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6."Differential Geometry (Dover Books on Mathematics" by Erwin Kreyszig
“Differential Geometry (Dover Books on Mathematics” Book Review: This book provides a clear and concise introduction to differential geometry of curves and surfaces in three-dimensional Euclidean space. It presents the topic in a simple and essential manner with detailed explanations, figures, and examples that convey the geometric significance, theoretical and practical importance of different concepts, methods, and results. The book focuses on the basic concepts and facts of analytic geometry, the theory of space curves, and the foundations of the theory of surfaces, along with fundamental problems. Topics covered include geodesics, mappings of surfaces, special surfaces, and absolute differential calculus. The book also includes problems with solutions to review the material presented and familiarize students with reasoning in differential geometry.

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7."Differential Geometry: A First Course" by D Somasundaram
“Differential Geometry: A First Course” Book Review: This book offers a classical introduction to the theory of space curves and surfaces for undergraduate and postgraduate courses in mathematics. It provides a detailed discussion on fundamental existence theorems and covers topics such as intrinsic properties, geodesics on surfaces, the second fundamental form with local non-intrinsic properties, and the fundamental equations of the surface theory with several applications. The presentation of the theorems and their proofs are clear and well-developed, making this book an illuminating insight into the essence of mathematics. It is highly recommended for readers seeking a comprehensive understanding of the topic.

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8."Differential Geometry (M.Sc)" by S G Venkatachalapathy
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9."A Course in Differential Geometry and Lie Groups (Texts and Readings in Mathematics)" by S Kumaresan
“A Course in Differential Geometry and Lie Groups (Texts and Readings in Mathematics)” Book Review: The book is presented in a clear and comprehensive manner, covering differential manifolds, tensor fields, Lie groups, integration on manifolds, and basic differential and Riemannian geometry. Geometric concepts are emphasized, providing readers with a practical understanding of the topic. Nontrivial examples and exercises are included, and there is a thorough discussion of the existence, uniqueness, and smooth dependence of solutions of ODEs. The book has a classical treatment with a modern approach and provides simple proofs to the hairy-ball theorem. It is suitable for a graduate-level introduction to basic differential and Riemannian geometry.

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10."Differential Geometry of Manifolds" by Khan
“Differential Geometry of Manifolds” Book Review: This book offers a precise and accessible exposition of the topic. It focuses on the mathematical formulation and solving problems using calculus techniques. The book covers a range of topics including algebra and calculus, Riemannian geometry, submanifolds and hypersurfaces, and almost complex manifolds, among others. The book is designed for postgraduate students of mathematics and researchers in the field of differential geometry, including those working in general theory of relativity, cosmology, and other applied areas. The book includes numerous examples and illustrations to aid understanding and provides a thorough treatment of the subject matter.

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11."A Comprehensive Introduction to Differential Geometry Vol. I" by M Spivak
“A Comprehensive Introduction to Differential Geometry Vol. I” Book Review: This comprehensive book offers an introduction to the topic of differential geometry, exploring concepts such as 2-dimensional manifolds, Riemannian and Lorentzian metrics, and the Levi-Civita connection. It also covers topics like orientations on manifolds, connections on vector bundles, Lie groups, Lie algebras, and more, providing a theoretical and mathematical understanding of these concepts. The book is intended for students and teachers in various fields of engineering and science seeking a detailed overview of differential geometry.

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3. Differential Geometric Methods in Control

 
1."A Comprehensive Introduce to Differential Geometry" by M Spivak
“A Comprehensive Introduce to Differential Geometry” Book Review: This book offers a comprehensive introduction to differential geometry, covering various topics such as differential structures, tensors, vector fields, integral manifolds, differential equations, differential forms, and integration. It also delves into Riemannian metrics, lie groups, topology, and other related concepts. Aimed at students, teachers, and professionals in engineering and science fields, this book provides an in-depth understanding of theoretical and mathematical aspects of differential geometry.

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2."Control Theory from the Geometric Viewpoint" by A Agrachev and Y. Sachkov
Book Review: This book presents a geometric approach to mathematical control theory, exploring various facts and methods related to the topic. It assumes a background in analysis and linear algebra, along with some familiarity with real and functional analysis, but does not require prior knowledge of control theory or differential geometry. The book offers clear explanations of dynamical systems, which are systems determined by initial conditions, and focuses exclusively on finite dimensional systems. Through its concise and accessible treatment, this book is ideal for students and professionals seeking to gain a deeper understanding of mathematical control theory.

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3."Geometric Methods in Inverse Problems and Pde Control" by Irena Lasiecka Gunther Uhlmann Croke Lasiecka Uhlmann
“Geometric Methods in Inverse Problems and Pde Control” Book Review: This book offers an in-depth exploration of geometric methods in inverse problems and PDE control, covering common techniques used in the study of inverse coefficient problems, as well as the control problems for partial differential equations. It showcases the application of geometric methods in diverse fields, including medical imaging, non-destructive testing, geophysical prospecting, and more. Intended for students, teachers, and professionals in engineering and science, particularly those in instrumentation, this book provides a comprehensive overview of the subject matter.

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4."Differential Geometric Methods in Mathematical Physics" by Heinz-Dietrich Doebner
“Differential Geometric Methods in Mathematical Physics” Book Review: This book offers a thorough introduction to the differential geometric methods in mathematical physics, with a focus on the classical field theory. It covers a wide range of topics including partial derivatives, critical points, immersion theorems, partition of unity, vector bundles, tangent bundle of a manifold, vector fields, alternating functions, wedge product, Frobenius integrability theorem, and more. It is designed to benefit students, teachers, and professionals from various fields of engineering and science seeking to deepen their understanding of differential geometric methods in mathematical physics.

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5."Applications of Analytic and Geometric Methods to Nonlinear Differential Equations" by Clarkson
“Applications of Analytic and Geometric Methods to Nonlinear Differential Equations” Book Review: This book presents a comprehensive review of the applications of analytic and geometric methods to nonlinear differential equations. It covers the inverse scattering transform (IST) using complex function theory and discusses twistor theory using differential geometry. It also offers solutions to self-dual Yang–Mills equations with detailed explanations. The book provides mathematical and theoretical explanations to frequently occurring problems. It is targeted at students, teachers, and professionals in various fields of engineering and science seeking to expand their knowledge of the subject.

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6."New Analytic and Geometric Methods in Inverse Problems" by Somersalo Erkki
“New Analytic and Geometric Methods in Inverse Problems” Book Review: This book offers a basic introduction to novel analytical and geometric techniques in inverse problems. It elucidates the concept of inverse problems by utilizing mathematical models and data from indirectly observed quantities. It explores various applications of inverse problems in different fields, including medical imaging, remote sensing, material testing, geosciences, and finance. The book targets students, educators, and experts in various areas of engineering and science.

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7."Geometric and Topological Methods for Quantum Field Theory" by Andrs Vargas
“Geometric and Topological Methods for Quantum Field Theory” Book Review: This book presents a detailed and comprehensive overview of the latest developments in geometric and topological methods in quantum field theory. It covers a wide range of topics, including geometry, topology, and quantum field theory. The book offers detailed discussions on knot invariants and configuration spaces. It also provides insights into Raimar Wulkenhaar’s contributions to Euclidean quantum field theory from a statistical perspective. The book is intended for students, teachers, and professionals in various fields of engineering and science.

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4. Differential Geometry of Manifolds

 
1."A Course in Tensors with Applications to Riemannian Geometry" by R S Mishra
“A Course in Tensors with Applications to Riemannian Geometry” Book Review: This book provides a comprehensive exploration of tensors and Riemannian geometry. It covers the laws of transformation of contra-variant vectors and delves into topics such as exterior algebra, tensor calculus, differentiable manifolds, and tangent vector spaces. The book includes examples and exercises to aid in understanding more advanced topics. A basic understanding of groups, rings, fields, and vector spaces is required. This book is recommended for students, professors, researchers, and professionals seeking a thorough understanding of tensors and Riemannian geometry.

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2."Differentiable Manifolds" by Y Matsushima
“Differentiable Manifolds” Book Review: This book presents a thorough and clear introduction to the theory of differential manifolds and Lie groups. It requires a prerequisite knowledge of point set topology, basic analysis, vector spaces, groups, and other algebraic elements. It is suitable for both advanced undergraduate and introductory graduate courses.

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3."Differential Geometry with Applications to Mechanics and Physics" by Y Talpiert
“Differential Geometry with Applications to Mechanics and Physics” Book Review: This comprehensive book covers differential geometry and its applications to mechanics and physics. It begins with an introduction to topology and differential calculus in Banach spaces, followed by a detailed discussion on differentiable manifolds, mapping submanifolds, and tangent vector spaces. Later chapters cover topics such as the tangent bundle, vector fields on manifolds, Lie algebra structure, and one-parameter group of diffeomorphisms. In addition, the book explains exterior differential forms, Lie derivative and Lie algebra, n-form integration on n-manifolds, and Riemann geometry. The book is packed with examples and solved exercises and can be used as a reference by students, teachers, and professionals in various fields.

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4."Differential Geometry Of Manifolds" by U C De and A A Shaiks
“Differential Geometry of Manifolds” Book Review: This book provides a thorough examination of the theory of differentiable and Riemannian manifolds, emphasizing the significance of the tangent vector in the study of differentiable manifolds. The theory of Riemannian geometry is elucidated in detail with the aid of numerous proofs. This book is suitable for postgraduate students and researchers in the field of differential geometry, particularly those interested in its applications to general relativity and cosmology.

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5."Differential Geometry of Manifolds" by Stephen T Lovett
“Differential Geometry of Manifolds” Book Review: The book provides an extensive coverage of the fundamental concepts of manifolds starting from curves and surfaces of differential geometry. It begins with an introduction to the Hamiltonian formulation and symplectic manifolds, and then progresses to the description of differentiable and Riemannian manifolds, integrating the classical and modern formulations. Additionally, it covers the basics of string theory, tensorial formulation of electromagnetism and general relativity. The book follows a practical approach and includes numerous examples and exercises for better comprehension of the subject. Appendices are provided, which include the required information on point set topology, calculus of variations, and multilinear algebra. This book is suitable for postgraduate students and researchers working in the field of mathematics and theoretical physics.

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6."MANIFOLDS AND DIFFERENTIAL GEOMETRY" by LEE J M
“Manifolds and Differential Geometry” Book Review: This book provides a comprehensive introduction to the tools and structures of modern differential geometry and manifolds. It covers topics such as vector bundles, tensors, differential forms, de Rham cohomology, the Frobenius theorem, and basic Lie group theory. Further chapters delve into the general theory of connections on vector bundles, the differential geometry of hypersurfaces in Euclidean space, and the derivation of the exterior calculus version of Maxwell’s equations. The fundamentals of Riemannian manifolds and Lorentz manifolds are covered under semi-Riemannian geometry. The book is aimed at graduate students, mathematicians, and teachers of mathematics.

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7."Differential Manifolds (Dover Books on Mathematics)" by Antoni A Kosinski
“Differential Manifolds” Book Review: This book provides a comprehensive treatment of the topological structure of smooth manifolds. It covers various topics including the technique of connecting manifolds along submanifolds, the handle presentation theorem, and the h-cobordism theorem, which are demonstrated through detailed explanations and proofs. The book also introduces the Pontryagin Construction, which links differential topology and homotopy theory, and discusses the classification of smooth structures of spheres using the method of surgery. Prior knowledge of elementary algebraic topology is assumed. This book is recommended for advanced undergraduate and graduate students interested in the systematic study of the topological structure of smooth manifolds.

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8."Differential Geometry: Manifolds, Curves, and Surfaces (Graduate Texts in Mathematics)" by Marcel Berger and Bernard Gostiaux
“Differential Geometry: Manifolds, Curves, and Surfaces” Book Review: This book is an updated and expanded edition of the 1972 book, “Geometrie Differentielle”. It covers a range of topics in analysis and geometry, with a particular focus on manifolds, curves, and surfaces. The book makes use of non-trivial examples to help readers become familiar with these concepts. Additionally, there are separate chapters dedicated to the detailed treatment of surfaces in three-dimensional space, both from mathematical and physical perspectives.

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9."Differential Geometry: Curves - Surfaces - Manifolds" by Wolfgang Kuhnel
“Differential Geometry: Curves – Surfaces – Manifolds” Book Review: This book is a comprehensive introduction to differential geometry that covers recent advances made in this field. The general theory of geometry of curves and surfaces is discussed, followed by the geometry of general manifolds including connections and curvature. The book is richly illustrated with numerous figures, and includes examples and exercises with solutions. A background in undergraduate analysis and linear algebra is necessary.

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5. Differential and Riemannian Geometry

 
1."Textbook of Tensor Calculus and Differential Geometry" by Nayak P K
“Textbook of Tensor Calculus and Differential Geometry” Book Review: This book is aimed at students of mathematics, both at the undergraduate and postgraduate level. It presents a comprehensive treatment of both geometry and tensors, providing a conceptual exposition of fundamental results in tensor theory. The applications of tensors to differential geometry, mechanics, and relativity are also covered. The book delves into N-dimensional Riemannian space, the characteristic features of Riemannian space, and intrinsic properties of surfaces. The properties and transformation of Christoffel symbols and intrinsic geometry of surfaces are also discussed. The book includes numerous solved examples and diagrams to facilitate better understanding.

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2."Differential Geometry (Dover Books on Mathematics)" by Erwin Kreyszig
“Differential Geometry (Dover Books on Mathematics)” Book Review: The target audience for this book is mathematics students at the undergraduate and postgraduate level. Its subject matter is the differential geometry of curves and surfaces in three-dimensional Euclidean space. The book covers fundamental concepts and facts of analytic geometry, the theory of space curves, and the foundations of surface theory. Moreover, it presents problems related to the first and second fundamental forms and utilizes tensor calculus to explore the theory of surfaces. The latter part of the book focuses on geodesics, mappings of surfaces, special surfaces, the absolute differential calculus, and the displacement of Levi-Cività. Throughout the book, the author emphasizes the significance of different concepts, methods, and results in both theory and practice.

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3."A Course in Differential Geometry and Lie Groups (Texts and Readings in Mathematics)" by S Kumaresan
“A Course in Differential Geometry and Lie Groups (Texts and Readings in Mathematics)” Book Review: The intended audience for this book comprises undergraduate and postgraduate mathematics students, and its main topic is the Course in Differential Geometry and Lie Groups. The book covers various topics, including Differential Geometry, the concept of Tangent Space, derivative of a map, and graph theory. Additionally, it delves into mappings of surfaces, special surfaces, and the absolute differential calculus. To facilitate comprehension, the book features a multitude of solved examples and diagrams. Furthermore, each chapter concludes with practice exercises aimed at enhancing understanding.

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4."Lectures on Classical Differential Geometry: Second Edition (Dover Books on Mathematics)" by Dirk J Struik
“Lectures on Classical Differential Geometry: Second Edition (Dover Books on Mathematics)” Book Review: This is a book intended for advanced undergraduate and graduate students. It provides a comprehensive overview of the classical theory of differential geometry, with a focus on fundamental concepts related to curves and surfaces. An appendix is also included, which briefly explains how Cartan’s method of Pfaffians can be applied to curve and surface theory. The book is richly illustrated, helping to enhance students’ visual understanding of geometry, and each chapter concludes with thought-provoking text and a selection of challenging problems to encourage deeper learning.

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5."An Introduction To Differential Geometry (Dover Books On Mathematics)" by T J Willmore
“An Introduction To Differential Geometry (Dover Books On Mathematics)” Book Review: This book is designed for advanced undergraduate and graduate students, as well as students of physics and engineering. Its focus is on introducing the methods of differential geometry and tensor calculus. Vector methods are employed to explore the classical theory of curves and surfaces, while an introduction to the differential geometry of surfaces in the large equips students with ideas and techniques relevant to global research. The book concludes by concentrating on the concept of a tensor, initially in algebra, followed by calculus. It covers the basic theory of absolute calculus and the fundamentals of Riemannian geometry. To facilitate comprehension, the book provides numerous worked examples and exercises throughout the text.

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6."Riemannian Geometry (Graduate Texts in Mathematics)" by Peter Petersen
“Riemannian Geometry (Graduate Texts in Mathematics)” Book Review: The intended readership of this book consists of advanced undergraduate and graduate students, as well as students of physics and engineering. Its subject matter is the techniques and theorems of Riemannian geometry. The book covers both the geometric and analytic aspects of Riemannian geometry, including coordinate calculations of connection and curvature. Moreover, it delves into curvature on Lie Groups and submersions, and incorporates variational calculus. Later on, it emphasizes the Koszul formula, a new formula that is easily recalled and coordinate-free. To help readers comprehend the material, the book includes multiple worked examples and exercises throughout the text.

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7."Elementary Differential Geometry (Springer Undergraduate Mathematics Series)" by A N Pressley
“Elementary Differential Geometry (Springer Undergraduate Mathematics Series)” Book Review: The target audience of this book comprises advanced undergraduate and graduate students, as well as students of physics and engineering. Its scope encompasses the differential geometry of curves and surfaces, incorporating linear algebra and multivariable calculus. Furthermore, the book delves into non-Euclidean geometry, parallel transport, and their applications. As the book progresses, it emphasizes topics such as map coloring, holonomy, and Gaussian curvature. To enhance understanding, the book features numerous worked examples and exercises throughout the text.

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8."Differential Geometry: Bundles, Connections, Metrics and Curvature (Oxford Graduate Texts in Mathematics)" by Clifford Henry Taubes
“Differential Geometry: Bundles, Connections, Metrics, and Curvature (Oxford Graduate Texts in Mathematics)” Book Review: This book is intended for advanced undergraduate and graduate students, as well as students of physics and engineering. Its aim is to cover the essential language of modern differential geometry and theoretical physics. It includes topics such as differential forms, vector fields, Lie groups, and Grassmannians. Furthermore, it delves into geodesics and Jacobi fields, as well as the classification theorem for flat connections. As the book progresses, it emphasizes the definition of characteristic classes, and introduces complex and Kahler geometry. To provide context and relevance, the book incorporates many classical examples and applications of Differential Geometry.

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9."Differential Geometry and Tensors" by K K Dube
“Differential Geometry and Tensors” Book Review: This is a book intended for advanced undergraduate and graduate students of mathematics, physics, and engineering. The book provides a comprehensive exposition of the fundamental results in the theory of tensors, covering concepts such as the precise derivation of tensors, associated tensors, and tensor transformations. Additionally, the book focuses on the tensor formulation of divergence and curl. Classical examples from differential geometry are included, along with numerous applications. This book is an excellent resource for students seeking to deepen their understanding of tensors and their applications.

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10."The Geometry of Spacetime: An Introduction to Special and General Relativity (Undergraduate Texts in Mathematics)" by James J Callahan
“The Geometry of Spacetime: An Introduction to Special and General Relativity (Undergraduate Texts in Mathematics)” Book Review: The target audience of this book is undergraduate students studying mathematics. The book encompasses both General and Special Relativity theories and introduces several mathematical tools including matrices, hyperbolic geometry formulae, vector calculus, linear algebra, and analysis. Later chapters cover topics such as Lorentz transformation techniques, 3D calculus, limits, and mappings from differing geometries. Additionally, the book explores Euclidean and spherical geometries and introduces concepts related to Newtonian gravitation. Throughout the text, worked examples and exercises are included to aid understanding.

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We have put a lot of effort into researching the best books on Geometry and came out with a recommended list and their reviews. If any more book needs to be added to this list, please email us. We are working on free pdf downloads for books on Geometry and will publish the download link here. Fill out this Geometry books pdf download" request form for download notification.

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