Sharing his appreciation for the beauty of such mathematical objects as Kleinian groups and hyperbolic knots, Bonahon (University of Southern California) first introduces 2-dimensional geometry in chapters of incremental difficulty. He then applies hyperbolic geometry to classical problems in 3-dimensional topology and treats the general Geometrization Theorem for 3- dimensional manifolds, whose proofs were recently developed. Appendices provide a "toolkit" of the prerequisite math and difficulty-rated further reading. Chapters include proofs for theorems, illustrations, and exercises. Published in association with the Institute for Advanced Studies, Princeton/Park City Mathematical Institute. Annotation ©2009 Book News, Inc., Portland, OR (booknews.com)