The serious student of general relativity will experience a constant need to learn more tensor calculus -- or in modern terminology, `differential geometry'. Some of this can be found in the texts listed above, but it is also good to read mathematics texts. Here are a few:
Gauge Fields, Knots and Gravity, J. C. Baez and J. P. Muniain (World Scientific, Singapore, 1994).
An Introduction to Differentiable Manifolds and Riemannian Geometry, W. M. Boothby (Academic Press, New York, 1986).
Semi-Riemannian Geometry with Applications to Relativity, B. O'Neill (Academic Press, New York, 1983).