I'm an undergraduate Math student and I am doing a side project for which I would like to study Differential geometry and its applications in general relativity. I have taken a few proof based courses including Analysis I, Introductory Number theory, Abstract Algebra.
I would like to get a text that isn't too far above what I have studied but still challenging and informative. Any suggestions are welcome.
Thanks
Wald's General Relativity.
It is a book from a Physicist to Physicists, but any reader will not be missing statements and proofs (or sketch of them). His approach is still akin to formulations using coordinates, although he manages to do it in a global way.