# Riemannian Geometry book to complement General Relativity course?

What would be a good Riemannian Geometry (or Differential Geometry) book that would go well with a General Relativity class (offered by a physics department)? I'm in one right now, but I'd like a pure math perspective on the math that's introduced as I can imagine, inevitably some things would be swept under the rug and I'd like a fuller picture. I'm looking at John M. Lee's "Riemannian Manifolds" and Jeffrey Lee's "Manifolds and Differential Geometry".

Are these books suitable? What parts should I study?

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Do you know Nakahara's book? –  Sigur Feb 5 '13 at 21:16
Nakahara is too terse for me. A lot of material thrown in the smallest amount of pages. But it is a good guide of the material I think. –  Sickell Feb 5 '13 at 21:28

STERNBERG_PDF and O'NEILL ${}{}{}{}{}{}{}$

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Thanks. The book by O'Neill looks great. –  Sickell Feb 5 '13 at 22:41
+1 for O'Neill. –  Neal Feb 5 '13 at 23:40