Because we don't teach geometry either when, or as deeply as we should, we do damage control instead. We offer "transition to abstraction" courses where students will first meet mathematical proof, but detached from any consistent content. Though such courses sometimes do other things well, they rarely achieve their stated aim--sound preparation for subjects such as abstract algebra, real analysis, and topology. Teachers of these advanced courses generally find that they must redo the principles of proof all over from scratch. Mathematical proof, isolated from substantial content, strikes most students only as a quaint conventionalized genre, like fugue or villanelle, with productions conforming to received rules that either win praise from the teacher or not, for mysterious reasons. This book by Burger (Williams College) will serve such courses better than many competitors. Though sufficiently accessible to reach the weakest students, he nevertheless avoids the trap of exercises that request purely hygienic proofs--formal verifications of statements no sentient person could doubt. Indeed, learning to value proofs should stand prior to learning to construct them, and already Burger's first chapter on puzzles sets the tone right, making it clear that mathematics holds surprises for us even in the simplest situations. Summing Up: Both books: Recommended. Upper-division undergraduates through faculty.