General Relativity overlaps mostly with Riemannian Geometry. This is because the theory concerns the metric of space-time. The field equations, for example, is a tensor equation determining the metric. There are many good texts for Riemannian Geometry but you could start with Klingenberg and pick up the prerequisite stuff as you go along. You should also be familiar with tensors and so get a good book on multilinear algebra. Spivak's books are good but there are 5 of them and they cover a lot of stuff that's not immediately relevant. Finally, you need to be relating this all back to physics. I think Misner, Thorne, and Wheeler's book Gravitation gives a good intro to the subject.