This volume is based on lectures notes for the courses delivered at the Cimpa Summer School: From Classical to Modern Probability, held at Temuco, Chile, be th th tween January 8 and 26 , 2001. This meeting brought together probabilists and graduate students interested in fields like particle systems, percolation, Brownian motion, random structures, potential theory and stochastic processes. We would like to express our gratitude to all the participants of the school as well as the people who contributed to its organization. In particular, to Servet Martinez, and Pablo Ferrari for their scientific advice, and Cesar Burgueiio for all his support and friendship. We want to thank all the professors for their stimulating courses and lectures. Special thanks to those who took the extra work in preparing each chapter of this book. We are also indebted to our sponsors and supporting institutions, whose interest and help was essential to organize this meeting: CIMPA, CNRS, CONI CYT, ECOS, FONDAP Program in Applied Mathematics, French Cooperation, Fundacion Andes, Presidential Fellowship, Universidad de Chile and Universidad de La Frontera. We are grateful to Miss Gladys Cavallone for her excellent work during the preparation of the meeting as well as for the considerable task of unifying the typography of the different chapters of this book.