General relativity, step by step. This is a mathematical description of the nuts-and-bolts of Einstein's general theory of relativity, with no gaps. I am concentrating on the nitty-gritty of tensor calculus including detailed derivations of tensor algebra, Christoffel symbols, and the Riemann curvature tensor. I will discuss black holes in some detail (the Schwarzschild metric), and plan to add discussion of gravitational waves and cosmology.