Title: the best
Product review: This is the best book I've seen covering geometry at this level. Coxeter was known as an apostle of visualization in geometry; many other books that cover this material just give you page after page of symbols with no diagrams. He motivates all the topics well, and lays out the big picture for the reader rather than just presenting a compendium of facts. This is a survey of a huge field, but he does a great job of focusing on the most important results. As other reviewers have noted, this book is not "introductory" in the sense of high school geometry; it's introductory in the sense of being the kind of book a college math major would use in his/her first upper-division geometry course. It doesn't presuppose a great deal of mathematical knowledge, but it probably isn't a book that one could appreciate without having already developed quite a high level of mathematical maturity.
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