When one is ready to tackle the details of general relativity, it is probably good to start with one of these textbooks:
Introducing Einstein's Relativity,
R. A. D'Inverno
(Oxford University Press, Oxford, 1992).
Gravity: An Introduction to Einstein's General Relativity,
J. B. Hartle (Addison-Wesley, New York, 2002).
Introduction to General Relativity,
L. Hughston and K. P. Tod
(Cambridge University Press, Cambridge, 1991).
A First Course in General Relativity,
B. F. Schutz
(Cambridge University Press, Cambridge, 1985).
General Relativity: An Introduction to the
Theory of the Gravitational Field,
H. Stephani
(Cambridge University Press, Cambridge, 1990).