Special reference for differential geometry I am not entirely sure how to formulate the question, but here it is. I am looking to start a self study on general relativity, and of course I need a good grasp on semi-riemannian geometry (I am currently using O' Neill's book). However, when I was still looking for references, I recall reading an answer here, in this site, which said something along the lines of "choose a book without those damn Christoffel symbols" (though I can't really find it again). The question was about differential geometry books, without any mention to G.R. Now, I've seen how Christoffel symbols are important in general relativity, and a friend of mine who has already studied it a little deeper said he doesn't really know how to  get around them. 
So, I guess my question is: is there a way to work on the theory of G.R. without those symbols or, more importantly, is there a book that does such a treatment? (sorry about this very odd question; I asked here on MathSX because I'm looking for something like O' Neill, a math book with references to physics)
 A: The Christoffel symbols are the coordinate representation of the covariant derivative, so they are inevitably going to crop up whenever you want to make an actual computation in coordinates. When people tell you to avoid them, they mean to avoid them when they are unnecessary - i.e. to use coordinate-free definitions and proofs whenever possible. Thus while it is possible to do much of the theory of GR without referring to Christoffel symbols, it would be silly for a book not to mention them at all, just as it would be silly for any physics text to omit examples.
With that clarified, I'd say O'Neill is what you're looking for - it's more abstract than any GR book I've looked through (I guess Wald is close) and does pretty much everything in the coordinate-free setting. The only times he uses Christoffel symbols is when giving explicit coordinate formulas, which are usually corollaries of the actual theorems.
Given that it combines this modern treatment of the geometry with a decent chunk of GR, I highly recommend it.
