This book is loosely based on Professor Soardi’s lectures and is an excellent introduction that discusses clearly and concisely the main points of wavelet theory. It is divided into seven chapters with the following headings: Multiresolution analysis in $L^2(R)$, Splines and multiresolution analysis, Wavelets, Compactly supported wavelets, Multidimensional wavelets, Wavelet frames, and Wavelets in signal processing. The bibliography is up to date and lists most of the important books on wavelets and its applications, together with a judiciously chosen sample of papers on the subject. A number of graphs enhance the presentation. Unfortunately, the book lacks an alphabetical index. The typographical layout is very nice, and the book is well made.
Richard A.Zalik (Auburn University)