# 100 Best Differential Geometry Books of All Time

We've researched and ranked the best differential geometry books in the world, based on recommendations from world experts, sales data, and millions of reader ratings. Learn more

Eric Weinstein[Eric Weinstein recommended this book on Twitter.] (Source)

Eric Weinstein[Eric Weinstein recommended this book on Twitter.] (Source)

Eric Weinstein[Eric Weinstein recommended this book on Twitter.] (Source)

Eric Weinstein[Eric Weinstein recommended this book on Twitter.] (Source)

The treatment begins with a chapter on curves, followed by explorations of regular surfaces, the geometry of the... more

**A contrarian argues that modern physicists' obsession with beauty has given us wonderful math but bad science.**

Whether pondering black holes or predicting discoveries at CERN, physicists believe the best theories are beautiful, natural, and elegant, and this standard separates popular theories from disposable ones. This is why, Sabine Hossenfelder argues, we have not seen a major breakthrough in the foundations of physics for more than four decades. The belief in beauty has become so dogmatic that it now conflicts with scientific objectivity: observation has been unable to... more

Barbara KiserThis is a firecracker of a book—a shot across the bows of theoretical physics. Sabine Hossenfelder, a theoretical physicist working on quantum gravity and blogger, confronts failures in her field head-on. (Source)

Eric Weinstein[Eric Weinstein recommended this book on Twitter.] (Source)

Eric Weinstein[Eric Weinstein recommended this book on Twitter.] (Source)

**Don't have time to read the top Differential Geometry books of all time? Read Shortform summaries.**

Shortform summaries help you learn 10x faster by:

- Being comprehensive: you learn the
**most important points in the book** - Cutting out the fluff: you focus your time on what's important to know
- Interactive exercises:
**apply the book's ideas to your own life**with our educators' guidance.

**A funny, insightful, and self-contained guide to Einstein's relativity theory and classical field theories--including electromagnetism**

Physicist Leonard Susskind and data engineer Art Friedman are back. This time, they introduce readers to Einstein's special relativity and Maxwell's classical field theory. Using their typical brand of real math, enlightening drawings, and humor, Susskind and Friedman walk us through the complexities of waves, forces, and particles by exploring special relativity and electromagnetism. It's a must-read for both devotees of the series and any... more

Eric Weinstein[Eric Weinstein recommended this book on Twitter.] (Source)

Designed for advanced undergraduate and graduate students, this text invites its audience to take a fresh look at previously learned material through the prism of tensor calculus. Once the framework is mastered, the student is introduced to new material which includes differential geometry on manifolds, shape optimization, boundary perturbation and dynamic... more

Originally drawn to Yaqui Indian spiritual leader don Juan Matus for his knowledge of mind-altering plants, bestselling author Carlos Castaneda soon immersed himself in the sorcerer’s magical world entirely. Ten years after his first encounter with the shaman, Castaneda examines his field notes and comes to understand what don Juan knew all along—that these plants are merely a means to understanding the alternative realities that one cannot fully embrace on one’s own. In... more

Fortunately for you, there's Schaum's Outlines. More than 40 million students have trusted Schaum's to help them succeed in the classroom and on exams. Schaum's is the key to faster learning and higher grades in every subject. Each Outline presents all the essential course information in an easy-to-follow, topic-by-topic format. You also get hundreds of examples, solved problems, and practice exercises to test your skills.

This Schaum's Outline gives you Practice problems with full explanations that reinforce... more

**Don't have time to read the top Differential Geometry books of all time? Read Shortform summaries.**

Shortform summaries help you learn 10x faster by:

- Being comprehensive: you learn the
**most important points in the book** - Cutting out the fluff: you focus your time on what's important to know
- Interactive exercises:
**apply the book's ideas to your own life**with our educators' guidance.

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*Riemannian Geometry*is an expanded edition of a highly acclaimed and successful textbook (originally published in Portuguese) for first-year graduate students in mathematics and physics. The author's treatment goes very directly to the basic language of Riemannian geometry and immediately presents some of its most fundamental theorems. It is elementary, assuming only a modest background from readers, making it suitable for a wide variety of students and course structures. Its selection of topics has been deemed "superb" by teachers who have used the text.

A significant... more

**Don't have time to read the top Differential Geometry books of all time? Read Shortform summaries.**

Shortform summaries help you learn 10x faster by:

- Being comprehensive: you learn the
**most important points in the book** - Cutting out the fluff: you focus your time on what's important to know
- Interactive exercises:
**apply the book's ideas to your own life**with our educators' guidance.

Eric WeinsteinFolks frequently ask “What are the books that changed your life?” If I tell them, they are usually radically disappointed. I find that curious. I just cleared out of an office, and these are 4 shelves of spines of books that mattered enough to me to bring home. So here they are. (Source)

*x*, and theorems on differentiation and antidifferentiation lead to a definition of the chain rule and examinations of trigonometric functions, logarithmic and exponential functions, techniques of integration, polar coordinates, much more. Clear-cut explanations, numerous drills, illustrative examples. 1967 edition. Solution guide available upon request. less

The treatment opens with an introductory chapter on fiber bundles that proceeds to examinations of connection theory for vector bundles and Riemannian vector bundles. Additional topics include the role of harmonic theory, geometric vector fields on Riemannian manifolds, Lie... more

**Don't have time to read the top Differential Geometry books of all time? Read Shortform summaries.**

Shortform summaries help you learn 10x faster by:

- Being comprehensive: you learn the
**most important points in the book** - Cutting out the fluff: you focus your time on what's important to know
- Interactive exercises:
**apply the book's ideas to your own life**with our educators' guidance.

*Classics Library*, lays the foundation for understanding an area of study that has become vital to contemporary mathematics. It is completely self-contained and will serve as a reference as well as a teaching guide.

**Volume 1**presents a systematic introduction to the field from a brief survey of differentiable manifolds, Lie groups and fibre bundles to the extension of local transformations and Riemannian connections. The

**second volume**continues with the study of variational problems on geodesics... more

**This text is intended for an advanced undergraduate (having taken linear algebra and multivariable calculus). It provides the necessary background for a more abstract course in differential geometry. The inclusion of diagrams is done without sacrificing the rigor of the material.**

**For all readers interested in differential geometry. less**

**Confusing d104books? Missed Lectures?**

Not Enough Time?

**Fortunately for you, there's Schaum's.**

More than 40 million students have trusted Schaum's to help them succeed in the classroom and on exams. Schaum's is the key to faster learning and higher grades in every subject. Each Outline presents all the essential course information in an easy-to-follow, topic-by-topic format. You also get hundreds of examples, solved problems, and practice exercises to test your skills.

**This Schaum's Outline gives you**

Practice problems with... more

**The scion of a political dynasty ushers in the era of big government**

Politics was in Benjamin Harrison's blood. His great-grandfather signed the Declaration and his grandfather, William Henry Harrison, was the ninth president of the United States. Harrison, a leading Indiana lawyer, became a Republican Party champion, even taking a leave from the Civil War to campaign for Lincoln. After a scandal-free term in the Senate-no small feat in the Gilded Age-the Republicans chose Harrison as their presidential candidate in 1888. Despite losing the popular vote, he trounced the... more

**Don't have time to read the top Differential Geometry books of all time? Read Shortform summaries.**

Shortform summaries help you learn 10x faster by:

- Being comprehensive: you learn the
**most important points in the book** - Cutting out the fluff: you focus your time on what's important to know
- Interactive exercises:
**apply the book's ideas to your own life**with our educators' guidance.

*Differential Manifolds*presents to advanced undergraduates and graduate students the systematic study of the topological structure of smooth manifolds. Author Antoni A. Kosinski, Professor Emeritus of Mathematics at Rutgers University, offers an accessible approach to both the h-cobordism theorem and the classification of differential structures on spheres.

"How useful it is," noted the

*Bulletin of the American Mathematical Society,*"to... more

Eric Weinstein[Eric Weinstein recommended this book on Twitter.] (Source)

The text begins with a substantial chapter offering background on the mathematics needed for the rest of the book. Subsequent chapters emphasize physical... more

**Don't have time to read the top Differential Geometry books of all time? Read Shortform summaries.**

Shortform summaries help you learn 10x faster by:

- Being comprehensive: you learn the
**most important points in the book** - Cutting out the fluff: you focus your time on what's important to know
- Interactive exercises:
**apply the book's ideas to your own life**with our educators' guidance.

*Topological Methods in the Theory of Functions of a Complex Variable*in the Annals of Mathematics Studies series in 1947.) One classical application of Morse theory includes the attempt to understand, with only limited information, the large-scale structure of an... more

*Classics Library*, lays the foundation for understanding an area of study that has become vital to contemporary mathematics. It is completely self-contained and will serve as a reference as well as a teaching guide.

**Volume 1**presents a systematic introduction to the field from a brief survey of differentiable manifolds, Lie groups and fibre bundles to the extension of local transformations and Riemannian connections. The

**second volume**continues with the study of variational problems on geodesics... more

Part one opens with considerations of functional determinants and matrices, advancing to systems of total differential equations, linear partial differential equations, algebraic foundations, and a geometrical... more

**Don't have time to read the top Differential Geometry books of all time? Read Shortform summaries.**

Shortform summaries help you learn 10x faster by:

- Being comprehensive: you learn the
**most important points in the book** - Cutting out the fluff: you focus your time on what's important to know
- Interactive exercises:
**apply the book's ideas to your own life**with our educators' guidance.

Written primarily for students who have completed the standard first courses in calculus and linear algebra, ELEMENTARY DIFFERENTIAL GEOMETRY, REVISED SECOND EDITION, provides an introduction to the geometry of curves and surfaces.

The Second Edition maintained the accessibility of the first, while providing an introduction to the use of computers and expanding discussion on certain topics. Further emphasis was placed on topological properties, properties of geodesics, singularities of vector fields, and the theorems of Bonnet and Hadamard.

This revision of the Second Edition...

moreThe author discusses topics where the interaction of physical and mathematical theories has led to... more

The author intended this book not only to develop the basic ideas of Riemann's theory of algebraic functions and their integrals but also to examine the related ideas and theorems with an unprecedented degree of rigor. Weyl's two-part... more

**Don't have time to read the top Differential Geometry books of all time? Read Shortform summaries.**

Shortform summaries help you learn 10x faster by:

- Being comprehensive: you learn the
**most important points in the book** - Cutting out the fluff: you focus your time on what's important to know
- Interactive exercises:
**apply the book's ideas to your own life**with our educators' guidance.

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* Includes significant state-of-the art material that reflects important advances, connecting robotics back to mathematical fundamentals in group theory and geometry

* An invaluable reference that serves a wide audience of grad students and researchers in mechanical engineering, computer science, and applied mathematics less

**Don't have time to read the top Differential Geometry books of all time? Read Shortform summaries.**

Shortform summaries help you learn 10x faster by:

- Being comprehensive: you learn the
**most important points in the book** - Cutting out the fluff: you focus your time on what's important to know
- Interactive exercises:
**apply the book's ideas to your own life**with our educators' guidance.

Many nontrivial and original problems (some with hints and solutions)

Standard theoretical material is combined with more difficult theorems and complex problems, while maintaining a clear distinction between the two levels less

*An Introduction to Differentiable Manifolds and Riemannian Geometry, Revised*has sold over 6,000 copies since publication in 1986 and this revision will make it even more useful. This is the only book available that is approachable by beginners in this subject. It has become an essential introduction to the subject for mathematics students, engineers, physicists, and economists who need to learn how to apply these vital methods. It is also the only book that thoroughly reviews certain areas of advanced calculus that are necessary to understand the subject. less

**Don't have time to read the top Differential Geometry books of all time? Read Shortform summaries.**

Shortform summaries help you learn 10x faster by:

- Being comprehensive: you learn the
**most important points in the book** - Cutting out the fluff: you focus your time on what's important to know
- Interactive exercises:
**apply the book's ideas to your own life**with our educators' guidance.