Modern electronic devices such as cameras and computers use (among others) the jpeg-format to store photographs. Millions of people employ such wavelet-based technology every day. In sharp contrast to that, only a few thousand people on the planet have a detailed understanding of the mathematics concerning the C*-algebras O_n even though (as the book under review shows) there is a strong relationship between the two.This book entertains and educates the reader with a high-precision tour connecting very current technological advances such as high-tech filters and compression methods, classical mathematics such as wavelets and probability theory and advanced, new mathematical methods such as non-commutative Hilbert space operator algebra applications. This book distinguishes itself by placing modern mathematics close to modern technology and by showing (again) that pure mathematics is not necessarily only for mathematics' sake. The author Palle E.T. Jorgensen is a world-class mathematician with a distinguished publication record. This is a book that *every* student of mathematics should read in order to be guided and motivated what courses to take, what other more basic books to read, and what research to pursue. This is a book that computer scientists, physicists and engineers should read. In my opinion, it could spawn new innovation, maybe no patents, but benefits for all of mankind.