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The foundation of the field of symbolic dynamics is generally credited to Jacques Hadamard, who used infinite symbol sequences in his analysis of geodesic flow on negatively curved surfaces in 1898. Hadamard's symbolic techniques were soon adopted and extended by other authors. However, the field had to wait forty years for its christening by Marston Morse and Gustav Hedlund, who provided the first systematic study of symbolic dynamical systems as objects of interest in their own right. This rather prescient paper at the dawn of the computer age set the stage for the mathematical analysis of codes and finite-alphabet communication systems using the techniques of dynamics and ergodic theory, most notably in the pioneering work of C.E. Shannon on the mathematical theory of communication. Fifty years after Hadamard applied symbolic techniques to dynamics, Shannon and others were applying dynamical techniques to symbols. In the fifty-odd years since then, symbolic dynamics has expanded its reach to apply, and be applied to, many areas. It has broken the confines of one dimension to encompass multi-dimensional arrays. The six chapters of this volume provide an introduction to the field as it is studied today and a sampler of its concerns and applications. They are expanded versions of the lectures given in the American Mathematical Society Short Course on Symbolic Dynamics and its Applications held in San Diego on January 4-5, 2002. I would like to take this opportunity to thank Jim Maxwell, Wayne Drady and the other AMS staff members who coordinated the short course and worked behind the scenes to make it run smoothly.

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