Nagell accomplishes a lot in 300 pages. He concentrates on interesting and deep results that can be obtained by elementary methods. In this respect, Nagell's text resembles Hardy and Wright's, but he includes 180 exercises. The exercises, he writes, "are not of a routine character but are really intended to supplement the theory with known and new results ...." Thus the book is for the serious student of mathematics. Some highlights: In the first chapter, Nagell proves the irrationality of e and pi. In chapters 2 and 8, he introduces the reader to asymptotic methods and gives an elementary proof of the Prime Number Theorem. Other chapters include very good introductions to cyclotomic polynomials and Diophantine equations of the second degree. In chapter 5, he determines the values of quadratic Gauss sums. In the context of Diophantine equations, Nagell also proves some results about unique factorization in several imaginary quadratic number fields.