Arithmetic Functions and Integer Products presents an algebraically oriented approach to the theory of additive and multiplicative arithmetic functions. This is a very active theory with applications in many other areas of mathematics, such as functional analysis, probability and the theory of group representations. Elliott's volume gives a systematic account of the theory, embedding many interesting and far-reaching individual results in their proper context while introducing the reader to a very active, rapidly developing field. In addition to an exposition of the theory of arithmetical functions, the book contains supplementary material (mostly updates) to the author's earlier two volumes on probabilistic number theory.