An analysis of wavelets as tools for science and technology. This second edition is revised to include completely rewritten chapters on three topics: wavelets and the study of turbulence; wavelets and fractals (which includes an analysis of Riemann’s nondifferentiable function); and wavelets in astronomy. A new chapter on data compression was the original motivation for the new edition, and it contains information on image processing. Several other chapters have been updated with comments, references, historical notes and new material. Three appendices have been added: a primer on filters; key results (with proofs) about the wavelet transform; and a complete discussion of a counterexample to a conjecture of Mallat on zero-crossings. In addition, the references have been expanded to a selection of more than 200 entries.