The last two subjects mentioned in the title "Wavelets" are so well established that they do not need any explanations. The first is related to them, but a short introduction is appropriate since the concept of wavelets emerged fairly recently. Roughly speaking, a wavelet decomposition is an expansion of an arbitrary function into smooth localized contributions labeled by a scale and a position pa­ rameter. Many of the ideas and techniques related to such expansions have existed for a long time and are widely used in mathematical analysis, theoretical physics and engineering. However, the rate of progress increased significantly when it was realized that these ideas could give rise to straightforward calculational methods applicable to different fields. The interdisciplinary structure (R.c.P. "Ondelettes") of the C.N .R.S. and help from the Societe Nationale Elf-Aquitaine greatly fostered these developments. This conference was held at the Centre National de Rencontres Mathematiques (C.I.R.M) in Marseille from December 14 to 18, 1987 and brought together an interdisciplinary mix of participants. We hope that these proceedings will convey to the reader some of the excitement and flavor of the meeting.