This voluminous (about 600 pages) book is divided into eight chapters. The first chapter deals with the most popular constants (including e, π, the Golden Mean). The remaining chapters are devoted to the constants associated with number theory, analytic inequalities, approximation of functions, discrete structures, functional iteration, complex analysis and geometry. At the lowest level, the books consist of relatively short (about three pages) subsections, treating a particular constant (or a host of similar constants). Here the motivation, definition and an overview of known results, relation to other constants as well as some historical background are given, however, no proofs at all. Each subsection is followed by a detailed bibliography which can direct the reader to all she/he would be interested in. The book certainly brings a huge amount of material which is very interesting to a wide mathematical audience.

Reviewer:

dpr