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I did some prior research on differential geometry, tensor calculus and variational mechanics and luckily Dover publishes really cheap but good books on these topics. My most recent purchases are:

-> Lectures on Classical Differential Geometry (Dirk Struik)

-> Lagrangian and Hamiltonian Mechanics (Calkin)

-> The variational principles of Mechanics (Cornelius Lanczos)

-> Vector and Tensor Analysis with Applications (Borisenko & Tarapov)

Some former threads mention Do Carmo but a quick glance in the ebook tells me it doesn't offer anything new.

Other books who are on my radar are "Geometry of Physics" by Theodore Frankel (hence why post is in this topic) and "Geometry, Topology and Physics" by Nakahara. Sadly I can't find pdf's of these to look into. (I always buy the books that I like, I just take precautions)

EDIT: I found Nakahara but for a geometry book, it doesn't contain a lot of geometrical pictures. I am looking for geometrical insights like for example Pythagoras visual proof:

https://mathoverflow.net/questions/...ch-technical-detail-and-so-little-enlightenme