Before diving into the details of general relativity, it is good to get oriented by reading some less technical books. Here are four excellent ones written by leading experts on the subject:
General Relativity from A to B, R. Geroch (University of Chicago Press, Chicago, 1981).
Gravity from the Ground Up: An Introductory Guide to Gravity and General Relativity, B. F. Schutz (Cambridge University Press, Cambridge 2003).
Black Holes and Time Warps: Einstein's Outrageous Legacy, K. S. Thorne (W. W. Norton, New York, 1995).
Space, Time, and Gravity: the Theory of the Big Bang and Black Holes, R. M. Wald (University of Chicago Press, Chicago, 1992).