This book contains the courses given at the Fifth School on Complex Systems held at Santiago, Chile, from 9th to 13th December, 1996, by researchers working on areas related to recent trends in Complex Systems, including dynamical systems, cellular automata, symbolic dynamics, spatial systems, statistical physics and thermo-dynamics. Scientists working in these subjects come from several areas: pure and applied mathematics, physics, biology, computer science and electrical engineering. Each contribution is devoted to one of the above subjects. In most cases they are structured as surveys, presenting an original point of view about the topic as well as showing mostly new results.