Here is a list of physics and mathematics books and materials I recommend, along with my comments.
Riemannian Geometry and Tensor Analysis, by P.K. Rashevsky
Online lectures on Topology by Frederic P. Schuller
While this course is a basic introduction to General Relativity, the first part offers a very interesting and clear introduction to topological spaces (which may differ slightly from standard textbooks), tangent spaces, and differential manifolds. It provides a comprehensive introduction to the mathematical tools for General Relativity. I'm usually reluctant to consider online courses, but this one stands out. It would be fantastic if the author wrote a book based on the course, of course, with more details included.