Literature:
 Freely downloadable lecture notes by S.M. Carrol, grqc/9712019.
 also as a book: S.M. Carrrol: Spacetime and Geometry: An Introduction to General Relativity, AddisonWesley, 2003
 Compact lecture notes with exercises, Jouko Mickelsson, Hkan Snellman, and Tommy Ohlsson: Relativity Theory, KTH, 2005 [kompendium]
Additional reading

C.W. Misner, K.S. Thorne, and J.A. Wheeler, Gravitation, Freeman, 1973. (A thorough introduction to the theory of relativity, both its mathematical methods and astronomical applications)

Einstein's original paper on general relativity, alberteinstein.info
 A more light text Notes Dunsby
Here are some problems from Jouko's book:
Problems