In my view, by far the best book on GR is known as MTW amongst those who study the subject. For everyone else it is “Gravitation” by Misner, Thorne and Wheeler. A web search on “MTW Gravitation” will turn up plenty of useful links.
It is now 50 years old so misses recent developments such as gravitational wave astronomy (though it does cover gravitational waves themselves), chunks of modern observational cosmology, more treatment of alternative theories to GR than would be taught these days, and so on. However, for a thorough grounding in GR it still can’t be beaten in my opinion.
Beware, though, that this is not a book for the faint-hearted dilettante. It’s roughly 1300 pages long, can do double-duty as a door stop, and assumes a background knowledge appropriate to a physics graduate. (That said, I don’t have a physics degree but Oxford chemistry appears to have been sufficiently rigorous.) Some sections are clearly marked as being at a significantly higher level of difficulty; all of these can be skipped without missing anything important for those who want a more gentle introduction.
Ken: sounds like you have the physics background to cope with this work. I’m pretty sure that you have a better grasp of classical electrodynamics than I, for example, based on what you write above.
