The other answers already mention many good textbooks about mathematical aspects of general relativity. However, two books still seem to be missing, which in my opinion are also quite good on this subject. Let me add them here:

• M. Kriele: Spacetime. Foundations of General Relativity and Differential Geometry. volume 59 of Lecture Notes in Physics Monographs. Springer, Berlin, Heidelberg, 1999.
• R. Sachs and H.-H. Wu: General Relativity for Mathematicians. volume 48 of Graduate Texts in Mathematics. Springer, New York, 1977.