# Self-StudyTextbook recommendations for Modern Differential Geometry for Physicists

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Please make a recommendation from the following 6 textbooks;

Nakahara, Topology, Geometry and Physics

Frankel, Geometry of Physics

Nash, Topology and Geometry for Physicists

Schutz, Geometrical Methods of Mathematical Physics

Lovelock, Tensors, Differential Forms and Variational Principles

Baez, Gauge Fields, Knots and Gravity

Isham, Modern Differential Geometry for Physicists

Which of these is pedagogically the easiest to learn from for self-study? What are advantages of each? Which of these has the most standard notation used by the majority of physicists today (I want to be able to read the literature afterwards)?

I have read that Nakahara is a concise read at a higher level than Frankel. It is also mentioned that Nakahara is a standard among physicists however from a quick search it seems Frankel is being used a lot in physics departments to teach differential geometry to adv undergraduates and graduates of physics. I do not know anything about Nash's book but I have seen it mentioned. For example, Physics 229 at Caltech has used Frankel, Nakahara and Nash over the years, depending on the instructor. I do not really know what other departments are using such as Princeton or other top IVY leagues, if you know please share with me. I know Schutz is a great relativist and has won the 2019 Eddignton medal for his research. I know Lovelock was a great relativist and has generalized Einsteins theory of gravity to what is now called Lovelock Gravity. John Baez is well known for his posts online but I do not know much more about him. Isham is an award winning physicist for his contributions to quantum gravity and relativity but I have read that it's a tougher read. Please share your opinions on these textbooks, I hope to get some useful feedback from experienced theoretical physicists. I would like to learn from the book which is most taught at the IVY leagues, the easiest for self-study, the most complete and also the one with a notation that aligns with what physicists use today in all fields such as relativity, condensed matter,....Thank you.

asked Jul 12, 2020
recategorized Jul 13, 2020

As this question ask for 7 books to be discussed, I would suggest to post each review separately in our Recommendations category

An answer box to the above question could then be used to just link to these detailled reviews...

As I just finished Frankel, I will probably be able to make a start soon ;-)

@Dilaton I look forward to your comments on Frankel as I was really interested in that one.

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