Here is a list of physics and mathematics books and materials I recommend, along with my comments.
Linear Algebra and Multi-Dimensional Geometry by N. V. Efimov & E. R. Rozendorn
This is a very good introduction to linear (vector spaces) and affine spaces, with very clear and comprehensive axioms of linear spaces, along with theorems and demonstrations. Additionally, there are chapters dedicated to tensors, including the notions of covariant and contra-variant transformations. There is a surprising chapter about a simple introduction to groups, but with a purpose — since the next chapter follows the definition of Euclidean space with the introduction of metrics and the metric tensor, followed by a dedicated chapter on pseudo-Euclidean spaces and hyperbolic group rotations, actually about Minkowski space used as a mathematical tool in special relativity.
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.