This volume contains the courses given at the CIMPA–UNESCO Summer School on Symbolic Dynamics and its Applications held at Universidad de la Frontera, Temuco, Chile, from January 6th to 24th, 1997. This School was devised for graduate students and high level undergraduate students interested in dynamical systems emphasizing symbolic dynamics.

The scientific committee was composed of François Blanchard (IML–CNRS–Marseille), Mike Boyle (University of Maryland at College Park), Mike Keane (CWI–Amsterdam), Alejandro Maass (Universidad de Chile), Servet Martínez (Universidad de Chile) and Arnaldo Nogueira (Universidade Federal do Rio de Janeiro).

The book is divided into eight chapters, each one corresponding to a course given at Temuco and devoted to a particular, active area of symbolic dynamics or some application to ergodic theory or number theory. Each author has used his own notation, so each chapter can be considered as an independent one, even though there exist natural relations between them. Each chapter has its own bibliography; all the references in this foreword can be found in at least one of these bibliographies.

By now the reader has understood that our aim was not to make a textbook on symbolic dynamics – such textbooks exist, one is due to D. Lind and B. Marcus (Cambridge U. Press, 1997) and another to B. Kitchens (Springer-Verlag, 1998) – but rather to present the reader with a sampling of what is going on in the field and around it.