Best Differential Geometry Books of 2025

The latest addition to the New York Times bestselling physics series, "General Relativity: The Theoretical Minimum," by Leonard Susskind and André Cabannes, provides a comprehensive introduction to Einstein's general theory of relativity. The book covers the necessary mathematics of Riemannian spaces and tensor calculus, delves into black holes, establishes Einstein field equations, and solves them to describe gravity waves. The authors provide vivid explanations that are approachable yet rigorous, making this a must-read for anyone seeking a deeper understanding of the universe's real structure.

Visual Differential Geometry and Forms: A Mathematical Drama in Five Acts by Tristan Needham is an exceptional book that offers an intuitive and visual exploration of differential geometry and forms. The book fulfills two principal goals: putting the geometry back into differential geometry and offering the first undergraduate introduction to differential forms that treats advanced topics in an intuitive and geometrical manner. The author deploys Newton's geometrical methods to provide geometrical explanations of the classical results, making it easy to understand. Overall, this book is a must-read for anyone interested in mathematics and its applications.

The "Geometry Part 2" Quickstudy Reference Guide by Bar Charts is an excellent resource for children learning geometry. This book is the second part of a series that covers the fundamental structure of geometry. It is designed to help children understand complex geometrical concepts in a simple and easy-to-understand manner. The book provides detailed explanations of the different types of shapes, angles, and lines, making it an ideal reference guide for children who are struggling with geometry. The book is well-organized and easy to navigate, making it a valuable addition to any child's bookshelf.

The "Geometric Formulas" Quick Study Guide by BarCharts, Inc. is a 6-page laminated guide that covers general terms, lines, line segments, rays, angles, transversal line angles, polygons, circles, theorems & relationships, postulates, and geometric formulas. This guide is an excellent resource for children learning geometry and provides a quick and easy reference for formulas and concepts. The layout is simple and easy to follow, making it a great study tool for students of all levels. Overall, the "Geometric Formulas" Quick Study Guide is a valuable addition to any student's bookshelf.

This graduate-level textbook on the theory of smooth manifolds provides an excellent introduction to the subject. The book covers a wide range of topics including smooth structures, tangent vectors, vector bundles, tensors, differential forms, Lie groups, Lie algebras, and more. The author uses a concrete approach with intuitive discussions and pictures to help readers understand abstract concepts. The second edition has been revised and reorganized, with new topics added. The book is a great resource for differential geometers and anyone interested in using manifolds in mathematical or scientific research.

The 8th Grade Math Workbook by Ace Academic Publishing is a comprehensive practice workbook that covers all the required Common Core Standards for this grade level. The book includes high-standard questions, carefully written to help students reason abstractly and quantitatively using various models, strategies, and problem-solving techniques. It also includes multiple tests for each topic, allowing students to practice all types of questions, including free response. Additionally, the book features detailed step-by-step answers to help students understand the topics and gain confidence in solving similar problems. Overall, this workbook is an excellent resource for students preparing for Common Core standardized exams.

The "Introduction to Manifolds" is a concise and accessible introduction to manifolds, which are higher-dimensional analogs of smooth curves and surfaces, and fundamental objects in modern mathematics. The author presents the theory of manifolds with the aim of helping the reader achieve a rapid mastery of the essential topics. This book is an excellent foundation for further study of geometry and topology. The text also contains many exercises, making it ideal for self-study. Overall, this book is highly recommended for graduate or advanced undergraduate students with minimal prerequisites in analysis and algebra.

The book "Lost in Math: How Beauty Leads Physics Astray" by Sabine Hossenfelder explores the modern obsession of physicists with beauty and elegance in their theories. The author argues that this obsession has hindered scientific progress and led to untestable theories. The book provides a well-informed take on the current situation in fundamental physical theory while being self-aware, dosed with acerbic wit, and often quite funny. Overall, this book is a thought-provoking read that challenges the dogmatic belief in beauty and encourages physicists to rethink their methods and embrace reality to discover the truth.

The book "Geometry of Deep Learning: A Signal Processing Perspective" is a comprehensive guide for students and researchers interested in understanding deep learning from a geometric perspective. The book presents a unified approach to deep learning, explaining it as an ultimate form of signal processing techniques that can be imagined. It covers classical kernel machine learning approaches, deep neural networks, and the latest tools such as attention, normalization, Transformer, BERT, GPT-3, and generative models like GAN, VAE, normalizing flows, optimal transport, among others. The book is interdisciplinary and will appeal to students and researchers in both engineering and mathematics. Overall, this book is a valuable resource for those seeking a deeper understanding of deep learning and its underlying principles.

A Comprehensive Introduction to Differential Geometry, Vol. 1, 3rd Edition is part of Spivak's 5 volume set and is considered a classic and the best resource for an in-depth study of differential geometry. The book covers a wide range of topics including curves, surfaces, manifolds, and Riemannian geometry. The author's approach is rigorous and comprehensive which makes it suitable for advanced undergraduate and graduate students. The book is published by Publish or Perish. Overall, this book is an excellent resource for anyone interested in differential geometry and is highly recommended.