and http://www.goldbart.gatech.edu/PostScript/MS_PG_book/bookmas...
These are sort of orthogonal to the OP's link, they're not covering analysis, abstract algebra and topology, instead they're covering dif eq, spectral analysis, probability/stats, linear algebra.
standard: https://www.amazon.com/Mathematical-Methods-Physicists-Seven...
gentler: https://www.amazon.com/Mathematical-Methods-Physical-Science...
another recent addition: https://www.amazon.com/Mathematical-Tools-Physics-Dover-Book...
"purer" than the rest: https://www.amazon.com/Mathematical-Physics-Chicago-Lectures...
"more fun" than the rest: https://www.amazon.com/Geometry-Physics-Introduction-Theodor...
this pair is probably the most rigorous and difficult of the bunch (at least from what i remember):
https://www.amazon.com/Classical-Mathematical-Physics-Dynami...
https://www.amazon.com/Quantum-Mathematical-Physics-Walter-T...
and the grand-daddy of them all
https://www.amazon.com/Methods-Theoretical-Physics-Internati...
[Osborne --- Advanced Mathematical Techniques: for Scientists and Engineers](http://www.amazon.com/Advanced-Mathematical-Techniques-Scien...)
and for a much more indepth, but less pedagogically useful (more of a reference) [Arfken --- Mathematical Methods for Physicists, Seventh Edition: A Comprehensive Guide](http://www.amazon.com/Mathematical-Methods-Physicists-Sevent...)
In addition anything by Penrose tends to target a lay audience, but quickly build up formalism and cover concepts interesting to even practicing physicists.
Like, if you'd like to really dive into it then you're going to need to go through a lot of textbooks first.
If you are moderately familiar with multi-variable calc, then here is a good book to get started down the GR hole: https://www.amazon.com/Mathematical-Methods-Physicists-Compr...
Suffice to say, yes, there have been a lot of grad students that have the exact same questions and issue that you currently have. Further, once they have reached the end of the mathematical education required to understand how space time works in the first few minutes of the universe, they focus those questions into the issues we have with inflation. Those issues mostly come from our lack of understanding about how GR and QM interact, so the first 10e-43 seconds or so. At least, that is my understanding. Physicists are welcome to tell me how dumb I am right now!