Which of these two books should I read first? Is one of them more advanced than the other? I'm planning to use them to self-study geometry. Thanks.
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If you are planning to self study and are just beginning geometry, I would recommend neither at this stage.
Geometry Revisted is from a specific viewpoint: Visiting Elementary Geometry from the viewpoint of transformations.
A snapshot of the backcover of Geometry Revisited:
So you will miss out on some portions which are not covered by this book.
Introduction to Geometry is an advanced book and presumes fairly high familiarity already.
Note: The books are excellent. I suggest you revisit Geometry Revisited after you have done some amount of study and then perhaps take a shot at Introduction to Geometry.
Having read it at some point myself, I can vouch for Geometry Revisited. It is an excellent book and ought be read at some point.
If your only choices to self learn were Geometry Revisited and Introduction to Geometry, then I would recommend Geometry Revisited.
Geometry Revisited is much more elementary, aimed at high-school teachers and bright high-school students or college frosh. For example, K. Strubecker wrote in his AMS Math Review
If you are talking about "Introduction to Geometry" by Coxeter and "Geometry Revisited" by Coxeter and Greitzer, the consensus seems to be that both of them are pretty advanced, but "Introduction to Geometry" is significantly more so, while "Geometry Revisited" is closer to something 'right after high school geometry class,' so I guess you should start with the latter (assuming you do have some geometry knowledge already).
Geometry Revisited has a much narrower domain of content than an Introduction to Geometry. If your goal is to get a sense of what different kinds of problems, techniques, and concepts geometry has evolved to deal with, Introduction to Geometry is a "dated" but somewhat comprehensive choice. (For example, the whole "world" of computational geometry came on the scene after Coexeter's book.) One typically does not read mathematics books from cover to cover and one can dabble in Introduction to Geometry to see some of geometry's many parts. If one has heavy sledding in places than looking at the wiki article of the topic causing trouble might help.