This is already the 8th revised edition of a book that has been very popular since its first edition in 1952. Its popularity is based on a very readable style of exposition. Since its 6th edition, the book has been enlarged with chapter VIII entitled Computers and Number Theory (written by James H. Davenport) containing some known applications of the topics (e.g. factorisation, random number generation and the RSA cryptographic method) presented in the preceding parts of the book. The publisher promises a companion website (www.cambridge.org/davenport) bringing state-of-the-art material on primality testing and the use of computers in number theory with more details on the latest advances and sample codes for important algorithms. An important part of the book consists of some useful historical comments and references making it very readable and useful for anyone interested in number theory.