What is the best book to learn general relativity for undergraduate and graduate students ? And why?
I learnt it quite quickly from Landau&Lifshitz vol. II. It comes to the point without much ado, and it's clearly written including the necessary tensor calculus (Ricci only, no modern Cartan formulation).
Then there's also Misner, Thorne, Wheeler, where you precisely get the more advanced method, and it's written in a way that it's fun. There's just a reprint of the original book, which is even at a fantastic price (in Germany it's just 60EUR, which is really a good price for such a voluminous physics textbook of this outstanding quality of content).
Another good choice, and a good alternative to MTW, because it's emphasizing the physicists' point of view over the geometers' point of view, is Weinberg's Gravitation and Cosmology.
If you are aiming also at cosmology, you should get a very new text since all the books I mentioned above a pretty much outdated given the enormous progress made in the field. Again, there's a book by Weinberg, Cosmology (2008).
I'd recommend Zee's book because it's fun to read, but also very complete and has a lot of modern topics.
I still have to look at Zee's GR book. I hesitate to look at any book by him after I regretted to have bought his QFT book (I've never before nor after regretted to have bought a QFT book, but in this case I have...).
As discussed in another thread on GR books, Zee's gravity book is much better than his QFT book.
However, I recommend Hartle's Gravity as a first text.
If it was fleshed out a bit more, I think Tevian Dray's Differential Forms and the Geometry of General Relativity would be the ideal way to teach the mathematics.
Look at Hartle. In my opinion, this is the best introductory book in GR
Look at this post
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