Visual Differential Geometry and Forms: A Mathematical Drama in Five Acts

The visualizations and fruit demonstrations were a welcome whimsical touch. The book is very thorough and presents material in an approachable manner. I would highly recommend this book for graduate students in math and physics who want an entertaining read chocked full of mathematical insight into differential geometry and some aspects of algebraic topology.

Ordinarily, I wait until I've read all or a lot of a book before I rate it. I am not very far in but am more than happy to give the book 5 stars for the great benefits and insights I have already received from it. Initially, I thought this might be a book with some nice illustrations while not all that substantive on the mathematics, and I was willing to buy it even then. (I'm reminded of that great canard that every book on topology either ends with the definition of a Möbius strip or is a personal communication to J.H.C. Whitehead.) Here, what a pleasant surprise to see the breadth and depth of the topics! And yet, written so naturally and agreeably that this book should be accessible to undergraduates. An outstanding example of what mathematics and mathematical exposition should be.

Explains the subject well and does not require too much in prerequisites — the first two Acts can be read by someone with only some calculus and linear algebra. The best part are the exercises where the reader is encouraged to construct shapes out of paper or peel strips off a fruit. These remind me of the science books I read as a child. Those exercises are fun and instructive

Geometry is put back into the development of differential geometry in this book.

This book is incredible. It almost reads like fiction in that it doesn't feel like work at all. I found it very hard to put down. There's also lots of cool pictures that make things clear

A majority of the book are derivations in 3D and analogies using simple geometries in R3. I would recommend this to an undergraduate student looking to get into GR, but it's not the best reference book.

I think this book should be recommended to math students as an excellent auxiliary tutorial and to physics student (who learn General Relativity) as a basic textbook in Differential Geometry.

I wish I had it when I took Differential Geometry years ago as an undergrad.