The subject "optical signal processing" can and should include all aspects of optics and signal processing. However, that is too large a scope for a textbook that, like this one, is intended as an introduction to the subject at a level suitable for first year graduate students of electrical engineering, physics, and optical engineering. There­ fore, the subject matter has been restricted. The book begins with basic background material on optics, signal processing, matrix alge­ bra, ultrasound and SAWs, and CCDs. One might argue about this choice of topics. For example, there already exist very good books on matrix algebra. However, matrix algebra is so important in sig­ nal processing, especially in connection with devices such as optical matrix processors, that it was felt that a review was essential. Also, the matrix algebra needed for systolic arrays and parallel computing has made great advances in recent years. My original intention was to write a single-volume textbook cov­ ering most of the fundamental concepts and applications of optical signal processing. However, it soon became apparent that the large amount of material to be included would make publication in a single volume impracticable. Therefore this volume treats the "fundamentals" and a second volume will appear dealing with devices and applications. This textbook was stimulated by a set of short courses that I have directed and lectured since 1976, as well as regular courses that I have taught at Rensselaer Polytechnic Institute since 1974.