Reddit mentions of The Geometry of Physics: An Introduction

the only thing that comes to mind is Frankel's geometry of physics

http://www.amazon.com/The-Geometry-Physics-An-Introduction/dp/1107602602

it's not really a math book as such (not the most rigorous proofs, and few at that) and it has way more.

i'm no expert though.

The links between topology, geometry and classical mechanics are fairly well documented in the other comments. Geometry and topology are fairly important in modern physics, at least what I've seen of it. General Relativity is the main example of where geometric ideas began to enter into physics. A good resource for this is Sean Carroll's GR notes and corresponding book. There are more advanced GR texts as well, like Wald's book.

There are also some books which deal directly with the links between physics and geometry, such as Frankels book, Szekeres, Agricola and Friedrich and Sternberg. Of these I own Szekeres book which is very good, and Frankels looks very good as well. The other two I am not sure about.

Geometric ideas do raise their head in more areas, as an example it is possible to formulate electromagnetism in terms of tensors or the hodge dual (see here). Additionally, and this is a bit beyond my knowledge, a friend of mine is working on topics in quantum field theory involving knot theory. I'm not exactly sure how this works but the links are certainly there.

Sorry if this all has more of a differential geometry flavour to it rather than a topological one, the diff geo side is what I know better. Hope that all helps. :)

I've become greatly interested in geometric concepts in physics. I would like some opinions on these text for self study. If there are better options, please share.

For a differential geometry approach for Classical Mechanics:
Saletan?

For a General self study or reference book:
Frankel or Nakahara?

For applications in differential geometry:
Fecko or Burke?



Also, what are good texts for Geometric Electrodynamics that includes spin geometry?

I could be interested in reading that paper, however I might need a discussion on the Atiyah-Singer Index Theorem first - It's something I haven't really had to use, but something I'd like to know.

My own personal interests lie in manifolds with special holonomy, and I'd be particularly interested in discussing G2 manifolds, if anyone else is.

Another, more basic, option would be Frenkel's 'Geometry of Physics' book, which has a lot of nice physics formulated in the language of differential geometry. This may be a good option for people with physics backgrounds with little formal DG training, as it does all of DG from scratch while being sure to tie all the math to physics (E&M, Lagrangian/Hamiltonian Mechanics, Relativity, Yang-Mills Theory etc.) Check it out here: https://www.amazon.com/Geometry-Physics-Introduction-Theodore-Frankel/dp/1107602602

Maybe this book?

Or a standard Riemannian geometry textbook like do Carmo might suit your needs.