As I understand it, it was (my nemesis genius) Carl Friedrich Gauss who first developed the foundations for tensor calculus, and later the subject was soaked up by Albert Einstein.
Perhaps you're getting closer to the introductory course in General Relativity, or your hands are already in the dirt. Most likely, in your early physics training, coordinates have been solidly grounded in intuition. But when the spacetime you're trying to describe twists and turns such that any coordinate system will eventually fail—time has come to take a detailed look at the logic and consequences of coordinate systems in general. Associate Professor Pavel Grinfeld does this very well, with a mathematical rigour suited to physicists.