Number theory is one of the few areas of mathematics where problems of substantial interest can be fully described to someone with a minimal mathematical background. With this in mind, Pollack (Mathematics, University of Illinois at Urbana-Champaign) presents a book for readers who want to explore elementary methods in modern number theory. (Readers do, however, need some familiarity with number theory at an undergraduate level and should have taken a first course in modern algebra.) The author begins with a thorough introduction to elementary prime number theory, including Dirichlet's theorem on primes in arithmetic progressions, the Brun sieve, and the Erdos-Selberg proof of the prime number theorem. He then turns to topics that are particularly attractive and accessible, including Gauss' theory of cyclotomy and its applications to rational reciprocity laws; Hilbert's solution to Waring's problem; and modern work on perfect numbers. Annotation c2009 Book News, Inc., Portland, OR (booknews.com)