Supplementary literature on General Relativity

Synge, J. L. Relativity: the general theory

Synge and Schild - Tensor calculus
derivation of pseudotensors

Schutz - Geometrical methods of mathematical physics
some very rare detailed explanations

Wald, R M. - General relativity
advanced reference, discusses quantum gravity

Weinberg, S. - Gravitation and Cosmology
energy-momentum tensor in detail; standard reference for cosmology

Hawking and Ellis - The large scale structure of space-time. Cambridge University Press, 1973
in order to present Hawking's famous results this book professionally and tersely derives all the theory from scratch

Misner, Thorne, Wheeler - Gravitation (1973)
for reference rather than introduction, contains an enormous amount of interrelated information

R. Geroch - General relativity from A to B
math-free book, last chapter brilliantly explains the what spacetime diagrams including little light cones actually say

D. Bressoud - Second year calculus
good to learn the Poisson equation from

Dodson, C. T. J. - Tensor geometry : the geometric viewpoint and its uses, Pitman,
detailed explanations for the beginner

Dubrovin et al. - Modern geometry: methods and applications, Vol. 1

Spivak, Michael. - A comprehensive introduction to differential geometry, Vol. 2
Riemannian geometry, but local results apply to relativistic metrics as well.

Besse, Arthur L. - Einstein manifolds, Springer-Verlag, 1987
math survey about Riemannian and complex geometry with constant Ricci curvature, but still interesting

Taylor, M. E. - Partial differential equations
modern maths relevant to GRT - PDEs on Riemann and Lorentz manifolds etc. - mostly in survey form