Warning : this question may be borderline with physics.stackexchange, but I would like a mathematician's point of view.
Lately, I've been working quite a lot with (among others) hyperbolic spaces, action of Lie groups, etc. which required me to buff up my knowledge in the area. I still do not feel comfortable with the subject, but at least I am starting to have some intuition.
So, I thought it could be a nice idea to learn a little about general relativity. The first reason is that I've wanted to learn its basics for quite a time, but have never found the "right" occasion. Now, I can add a second reason : to get more familiar with the underlying mathematical objects.
So, what would would be a nice reference to learn the general theory of relativity? In my case, this would entail:
to be self-contained (i.e. for the physics side, no theoretical requirement beyond classical mechanics and electromagnetism) ;
to contain a high-level mathematical exposition.
Bonus points if the history of the theory and some important experiments are explained. Exercises are nice, too.