The volume under review is dedicated to the celebrated mathematician Paul Erdős. It is pointed out that during a lecture in 1985, Erdős said: « You don’t have to believe in God, but you should believe in The Book. » This volume was conceived in consultation with Erdős, who also suggested some of the Book’s contents. The presentation is very clear and it includes portraits, diagrams, and many historical comments. The sections treat results drawn from number theory, geometry (mainly combinatorial), analysis, combinatorics, and graph theory. Many of the proofs are due to Erdős himself. The volume includes many delicious topics in mathematics, including: proof that e is irrational (also showing the irrationality of certain related numbers); six proofs of the infinitude of the primes, including Euclid’s and Furstenberg’s Monsky’s theorem; Hilbert’s equidecomposible polyhedra problem; a decade-old proof of Fermat’s two-square theorem; applications of Euler’s formula V-E+F=2; the art gallery theorem; Sylvester’s problem on lines determined by pairs of points; maximizing the number of touching pairs of d-simplices; Hall’s marriage theorem; a Dinitz coloring problem for an ntimes n chessboard; probabilistic combinatorics, etc. The exposition is overall at once very clear, precise, stimulating and readable. The writing is lively, the material is diverse and maintains a strong unity. On balance, the book is a very useful contribution to the growing literature on this circle of ideas. The reviewer would encourage anyone with an interest in the beauty of mathematics to have this book in his or her personal library. The volume has had four editions in English, and has been translated into French, German, Persian, Hungarian, Italian, Japanese, Chinese, Polish, Portuguese, Korean, Turkish, Russian and Spanish. (ZDM/Mathdi)