MTW's Gravitation is regarded by many universities as the standard graduate-level book on General Relativity. However, is the methodology of the book of contemporary character? The cosmology part of the book appears to be somewhat dated. Is it so?
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$\begingroup$ The question is specific to a specific book, while the dupe isn't. Thus, I vote to reopen. $\endgroup$– peterhCommented Jan 1, 2017 at 23:44
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1$\begingroup$ Also, the dupe is a dupe of another that deals just with mathematical treatments of GR, with emphasis on more math than physics. That's why MTW became so primary, a very thorough math treatment from the point of view of physics, and a very thorough treatment of the physics, with plenty examples and physical areas. IMO there is no good replacement, and it's time there was one more up to date. Wald is like a little brother to MTW, lots less detail and a more succint math treatment, but much less worked out and in the end not enough for a great textbook. And too many words, not enough diagrams. $\endgroup$– Bob BeeCommented Jan 2, 2017 at 2:27
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3$\begingroup$ Note that Phys.SE usually do not provide reviews. MTW's Gravitation is often considered a bible in GR, and we might make an exception with it. For discussion go to the hbar chat room. $\endgroup$– Qmechanic ♦Commented Jan 2, 2017 at 11:28
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I have a particular opinion of MTW, which is that while it provides the complete background for GR, Hawking and Ellis has a technically pleasing approach. And while I don't personally recommend a first-reader to Hawking and Ellis (which was published in the same year as MTW) and instead recommend Wald or Carroll; Tong's notes are great as well. But everyone interested in GR has to read Hawking and Ellis, and while I doubt anyone can do so as a first-reader, it is definitely perfect to understand the state of GR from around 1955-1973, since it captures the Cauchy problem in GR and singularity theorems (and a particularly elegant chapter on black holes). In terms of the mathematical level of not-pacing-down, Hawking and Ellis wins over all, while MTW takes a more lenient approach without leaving out any mathematical formalities. As of methodologies, it has, like I said, a particularly lenient and slow-paced approach without pointing to the mathematics as sharply as Hawking and Ellis.