The book communicates with the reader not by the introduction of the topics but rather in the manner by which the topics are presented. Every major concept is developed by a three stage sequential process. First, the concept is introduced by an intuitive development which is usually pictorial in nature. Second, a non-sophisticated (but theoretically sound) mathematical treatment is developed to support the intuitive arguments. The third stage consists of practical examples designed to review and expand the concept being discussed. It is felt that this three step procedure gives meaning as well as mathematical substance to the basic properties of the FFT. The book should serve equally well to senior or first year graduate stu- dents and to the practicing scientific professional. As a text, the material covered can be easily introduced into course curriculums including linear systems, transform theory, systems analysis, signal processing, simulation, communication theory, optics, and numerical analysis. To the practicing engineer the book offers a readable introduction to the FFT as well as providing a unified reference. All major developments and computing procedures are tabled for ease of reference.