This book began as notes for a collection of lectures given as a graduate course in the summer semester (April to July) of 1993 at the Swiss Federal Institute of Technology (ETH), Zurich, building on a talk that I gave in Brazil in 1992. Subsequently, in the fall of 1995 and again in the spring of 1998, the course notes were extensively revised and expanded for an advanced topics course in the Department of Electrical and Computer Engineering at the University of Illinois, from which course has evolved the final form of the book that appears here. These lectures were also given in various forms at Eindhoven University, Michigan Technological University, Binghamton University, Washington University, and the Technical University of Vienna. The candid reactions of some who attended these lectures helped me greatly in developing the unique (perhaps idiosyncratic) point of view that has evolved, a view that insists on integrating recent developments in the subject of algebraic codes on curves into the classical engineering framework and terminology of the subject of error-control codes. Many classes of error-control codes and their decoding algorithms can be described in the language of the Fourier transform. This approach merges much of the theory of error-control codes with the subject of signal processing, and makes the central ideas more readily accessible to the engineer.