Dear Physics Forum personnel, Is it possible to learn differential geometry simultaneously while learning the relativity and gravitation? I have been reading Weinberg's book (currently in Chapter 02), but I believe that modern research in relativity is heavily based on the differential geometry and algebraic topology, which I did not master yet. I would like to learn them alongside with relativity, which will help me to prepare for upcoming theoretical research in relativity. I was thinking about studying differential geometry first, but it would be inefficient in time-wise as I am not convinced that I need thorough knowledge in it, at least from my experience with Weinberg. I have strong background in set-theoretic topology (Engelking) and algebra (Lang, Aluffi, Isaacs), but my memory of single-variable analysis and multilinear algebra are quite foggy....Also, I only have practical knowledge in vector calculus.