20 Best General Relativity Books for Beginners

Are you looking for the best General Relativity books to start your studies in the Theory of Relativity? Relativity, Spacetime, Gravitational Theory, Quantum Mechanics and String Theory, etc., are some of the most important branches of advanced physics. If you are looking to have a career in these, these General Relativity books for beginners may be the perfect spot for you.

Here is my pick for the 20 best general relativity books for beginners:

1. Spacetime and Geometry (Sean M. Carroll)

Spacetime and Geometry is an introductory textbook on general relativity for students, providing a solid foundation of the theory and mathematical formalism. It discusses three prominent applications of general relativity – black holes, cosmology, gravitational waves, and perturbation theory. It features details of the Einstein equation (how spacetime curves) and the geodesic equation (how matter moves through it).

If you want to learn the modern view of the expansion of the universe, what black holes are, and how gravitational waves are generated and detected, then this is an excellent resource for you. It also offers a concise introduction to quantum field theory in curved spacetime. After reading this book, you will be able to solve research-level problems in gravitational physics.

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2. Einstein Gravity in a Nutshell (A. Zee)

If you are looking for an accessible introduction to Einstein’s general theory of relativity, then this book is an excellent choice for you. A. Zee takes readers from the fundamentals of Newtonian mechanics to prominent areas of modern research like the Kaluza-Klein theory, brave worlds, and de Sitter and anti-de Sitter spacetimes. Notably, it emphasizes the group theory and action principle as guides in constructing physical theories.

The book takes a friendly approach to the necessary mathematics and also includes anecdotes from the history of physics to make it more engaging for students. It discusses black holes and associated topics, such as Hawking radiation, in great detail. It is an ideal textbook for both undergraduate and graduate students.

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3. General Relativity from A to B (Robert Geroch)

General Relativity from A to B is an especially great resource for readers who have had an introductory course in physics. If you want to gain from the accurate and deep elucidation of general relativity basics, you should definitely consider going for this book. It is written in lucid prose, features limited equations, and focuses a lot on fundamental concepts. The first half of the book deals with the notion of space and time in terms of Galilean and Aristotelian points of view. In contrast, the second half describes how the ideas of elapsed time (interval) and spatial distance are incorporated into space-time as geometrical entities. If you are a patient reader, you will definitely find this book rewarding.

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4. A First Course in Differential Geometry: Surfaces in Euclidean Space (Lyndon Woodward, John Bolton)

Differential geometry is the study of curved spaces using calculus techniques and the language used by Einstein to express general relativity. This is an introductory textbook that was originally written for a popular course given to third-year students at Durham University for more than 20 years. It offers a detailed introduction to differential geometry as studied by Gauss – curves and surfaces in the Euclidean space. The main topics included here are the classics of differential geometry (everything from Gaussian curvature to the Gauss-Bonnet theorem), but the book focuses on taking direct routes to explain, prove, and apply the main results. It has several exercises to give students a chance for self-assessment as well.

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5. Introduction to General Relativity, Black Holes, and Cosmology (Yvonne Choquet-Bruhat)

This is an introductory textbook aimed at students of mathematics interested in physics, as well as students of physics interested in exact mathematical formulations. It aims to provide an accurate description of the foundations and prominent consequences of general relativity. The author does not demand any specialized knowledge of physics from readers and properly describes recent interesting experimental and observational results which confirm the theory.

The mathematical level of Part A is intended for undergraduate students and could serve as a basis for a course on general relativity. Part B, despite being advanced, does not really require complicated mathematics either. The book is an excellent resource to follow the modern mathematical progress in the development of the latest cosmological and astrophysical observations.

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6. A Student’s Manual for A First Course in General Relativity (Robert B. Scott)

This is a detailed student manual written as an accompaniment to the bestselling textbook by Bernard Schutz, A First Course in General Relativity. With the help of its comprehensive solutions, you will be able to master general relativity through problem-solving whether you are a self-learner, undergraduate, or postgraduate.

It guides readers through every step of more than two hundred exercises, with simple and easily understandable derivations. It also features comprehensive solutions to nearly half of Schutz’s exercises and 125 fresh supplementary problems that deal with the subtler points in every chapter. It comes with a detailed index and collects helpful mathematical results like transformation matrices and Christoffel symbols for commonly studied spacetimes in an appendix.

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7. Introduction to General Relativity (Gerard ‘t Hooft)

Introduction to General Relativity presents general relativity as a scheme to describe the gravitational field and the equations obeyed by it. The book starts out from physical motivations, and then introduces curved co-ordinations before the notion of an affine connection field is added. The matrix field is eventually introduced as well. Thus, the readers are clearly able to see how space and time get more and more structured until Einstein’s field equations emerge logically. Several applications of the theory are mentioned, with special emphasis laid on an application on gravitational radiation. The book is a great option for an elementary course in general relativity.

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8. Gravity from the Ground Up: An Introductory Guide to Gravity and General Relativity (Bernard Schutz)

Considering the fact that this book has been written by a renowned expert in relativity who is well-known for his clearly written advanced textbooks, it surprisingly uses only high-school level mathematics and some optional computer programs to describe the laws of physics dealing with gravity, from Newton to Galileo to Einstein. It serves as a great resource for an accessible introduction to general relativity and astronomy. Instead of simply describing the universe, the author has made significant efforts to explain it in detail as well.

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9. Digestible Quantum Field Theory (Andrei Smilga)

Digestible Quantum Field Theory, as its name suggests, provides an intermediate-level treatment of quantum field theory. It is aimed at readers having a first degree in physics and a working knowledge of quantum mechanics and the special theory of relativity. It gives you a basic understanding of the quantum field theory without going into details of the actual calculations involved.

After a brief introduction, the author provides a broad survey of the universe and explains how the ideas of quantum field theory developed during the last century. Basic facts of relativity, analytical mechanics, quantum mechanics, and mathematics have also been provided. The book also describes the standard model, supersymmetry, and the mysterious realm of quantum gravity.

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10. General Relativity for the Intelligent, Resolute Amateur (Dr. Herbert Roseman)

Unlike most presentations of general relativity for amateurs, this book describes the subject in its natural language – mathematics. Starting with basic calculus, it develops the mathematics of curved space, tensors, Einstein’s field equations and their solutions. After that, the author brings up the classic problem of the precession of the perihelion of Mercury. He also discusses modern problems in physics like cosmology, inflation, black holes, gravitational lensing, and gravitational waves. The book has been written in a way that intelligent amateurs are able to understand Einstein’s authentic version of general relativity. It also features five short philosophical essays related to Einstein and general relativity.

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11. General Relativity and its Applications (Valeria Ferrari, Leonardo Gualteri, Paolo Pani)

General Relativity and its Applications features the latest groundbreaking discoveries in the field. It outlines the basics of Einstein’s theory of gravity and focuses on its most important astrophysical consequences, such as black holes, stellar structures, and the physics of gravitational waves. It combines advanced topics with mathematical tools, pedagogical boxes, examples, and practical applications of the theory. Thus, it provides immense learning opportunities and is a great choice for graduate and master students in astronomy and physics.

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12. A Short Course in General Relativity and Cosmology (Reinhard Hentschke, Christian Hobling)

This book is intended as a foundation for students to read and understand the textbooks and various scientific papers on general relativity and cosmology. It doesn’t simply answer questions in a qualitative manner; instead, readers are taught and encouraged to do calculations on their own, check the numbers, and answer the theoretical questions by themselves as well. The text’s brevity sans neglect of scope or mathematical accessibility of key points is really remarkable. The authors use the required mathematical concepts to help the reader gain a solid understanding of a very important part of modern physics along the shortest possible path. It is a good choice of text for the upper-undergraduate curriculum.

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13. Special and General Relativity: A Beginner’s Introduction to Basic & Advanced Concepts (Preetinder Rahil)

Relativity is one of the greatest achievements of the human mind, but can be a difficult theory to understand. This book by Preetinder Rahil serves as a bridge between detailed textbooks on relativity and comparatively simpler books intended for beginners. It aims to explain the intuition and meaning behind the mathematics and concepts of relativity.

It makes innovative use of analogies from daily life to develop intuition and visualization. Even if you are a beginner with a limited background in mathematics and physics, this is a great choice for you. Notation, which is a kind of language in itself, often proves to be the greatest obstacle in learning relativity. This book elegantly explains the reason and meaning behind relativistic notation.

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14. Modern Differential Geometry for Physicists (Chris J. Isham)

This new edition of the classic text Modern Differential Geometry for Physicists features a new chapter that introduces some of the elementary ideas of general topology required in differential geometry. These lecture notes are related to an introductory course on modern differential geometry without involving coordinates, taken by students attending the M.Sc. courses “Quantum Fields and Fundamental Forces” at Imperial College or first-year theoretical physics Ph.D. students. The book almost exclusively deals with mathematics proper, the detailed topics and emphasis have been selected keeping in mind how differential geometry is applied to modern theoretical physics.

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15. Introduction to Cosmology (Matts Roos)

Introduction to Cosmology offers a compact and introductory study of cosmology. It begins from fundamental principles and the ancient history of cosmology, before progressing to curved spacetimes, the thermal history of the universe, gravitational lensing, general and special relativity, and cosmological models including black holes, extended gravity models, and much more.

It features all-new theoretical approaches and richly detailed material on observational astrophysics and elaborated sections on astrophysical phenomena. There are numerous engaging illustrations and detailed references with problems at the end of every chapter. It is an excellent book for undergraduate students in astrophysics and physics taking a first course in cosmology.

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16. General Relativity: Basics and Beyond (Ghanashyam Date)

This book introduces students and budding researchers to the elementary concepts of general relativity, along with some of its more advanced aspects. It employs the pedagogical style of a standard textbook and features necessary ideas and sufficient background material required by readers to understand the issues and modern research.

The first five chapters serve as the core of an introductory course on general relativity, and then the book moves on to more complicated features of the topic. After discussing gravitational waves, cosmological spacetimes, and black holes, the author describes the evolutionary interpretation for the class of globally hyperbolic spacetimes, numerical relativity, and various approaches which are aimed at the challenges of general relativity.

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17. General Relativity: A Concise Introduction (Steven Carlip)

Einstein’s general theory of relativity is important for both specialists and a much wider group of physicists. This concise textbook on gravitation and general relativity by Steven Carlip introduces students to the sprawling landscape of science which is related to general relativity. It also features some of the latest research in the field.

If you are interested in physics – be it condensed matter theory, high energy physics, gravitational radiation or cosmology – you will certainly find this book appealing. Apart from the “standard” topics included in most introductory textbooks, it also features brief introductions to more advanced topics. The final chapter provides guidance for further study, from quantum gravity to mathematical relativity.

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18. A Primer in Tensor Analysis and Relativity (Ilya L. Shapiro)

This is an undergraduate textbook which offers a simple and easy-to-understand introduction to tensor algebra and analysis. It also deals with both general and special relativity. Featuring a large number of explanations, exercises and examples, it is a wholesome book for any related course.

It is divided into three different parts based on lecture notes that have been carefully restructured for classroom teaching over the past two decades. It features explanations of technical material that is quite difficult to come across elsewhere, such as an accessible description of Riemann normal coordinates and conformational transformations. It is a great resource for mathematicians and future experimental and theoretical physicists.

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19. Relativity: A Journey Through Warped Space and Time (Daniel R. Mayerson, Anthony M. Charles, Joseph E. Golec)

In this book, you will find excellent explanations of concepts related to general and special relativity for newcomers. It can serve both as an introduction to the subject for high school students and a helpful guide for undergraduate students who wish to get started with Einstein’s theories. It features numerous exercises and engaging illustrations to help readers grasp the topics better.

The topics included here are Lorentz transformations, time dilation & length contraction, the twin paradox and other paradoxes, the Einstein equivalence principle, geodesics, Minkowski spacetime, curvature of space and spacetime, Einstein’s equations of general relativity, parallel transport, cosmology, wormholes, black holes, time machines, gravitational waves, and many more.

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20. From Special Relativity to Feynman Diagrams (Riccardo D’Auria, Mario Trigiante)

From Special Relativity to Feynman Diagrams serves as an introductory course on theoretical particle physics, and aims to fill the gap between basic courses of quantum and classical mechanics and advanced courses of field theory and relativistic quantum mechanics. It begins with a brief but comprehensive introduction to special relativity and then takes up important concepts of relativistic dynamics and some basic aspects of general relativity.

It explains the fundamentals of the theory of groups and Lie algebras and discusses the group of rotations and the Poincare and Lorentz groups. It also offers a short account of tensor calculus and representation theory. The last four chapters deal with the development of the quantum field theory, finally introducing the graphical description of interaction processes with the help of Feynman diagrams. It is a great option for lecturers, engineers, and students who want to understand the main concepts which form the basis of modern theoretical particle physics.

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Gaurav Tiwari

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