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The function of a filter is to transform a signal into another one more suit- able for a given purpose. As such, filters find applications in telecommunica- tions, radar, sonar, remote sensing, geophysical signal processing, image pro- cessing, and computer vision. Numerous authors have considered deterministic and statistical approaches for the study of passive, active, digital, multidimen- sional, and adaptive filters. Most of the filters considered were linear although the theory of nonlinear filters is developing rapidly, as it is evident by the numerous research papers and a few specialized monographs now available. Our research interests in this area created opportunity for cooperation and co- authored publications during the past few years in many nonlinear filter families described in this book. As a result of this cooperation and a visit from John Pitas on a research leave at the University of Toronto in September 1988, the idea for this book was first conceived. The difficulty in writing such a mono- graph was that the area seemed fragmented and no general theory was available to encompass the many different kinds of filters presented in the literature. However, the similarities of some families of nonlinear filters and the need for such a monograph providing a broad overview of the whole area made the pro- ject worthwhile. The result is the book now in your hands, typeset at the Department of Electrical Engineering of the University of Toronto during the summer of 1989.