This book is devoted to recent developments in symbolic dynamics, and it comprises eight chapters. The first two are concerned with the study of symbolic sequences of "low complexity," the following two introduce "high complexity" systems. Chapter five presents results on asymptotic laws for the random times of occurrence of rare events. Chapter six deals with diophantine problems and combinatorial Ramsey theory. Chapter seven looks at the dynamics of symbolic systems arising from numeration systems, and chapter eight gives a complete description of the symbolic dynamics of Lorenz maps.

This book contains the lectures given at the II Canference an Dynamics and Randamness held at the Centro de Modelamiento Matematico of the Universidad de Chile, from December 9th to 13th, 2002. This meeting brought together mathematicians, theoretical physicists, theoretical computer scientists, and graduate students interested in fields related to probability theory, ergodic theory, symbolic and topological dynamics. We would like to express our gratitude to an the participants of the conference and to the people who contributed to its orga nization. In particular, to Pierre Collet, BerIiard...