The core of the material on large scale dynamics of interacting particles grew out of courses I taught at the Katholieke Universiteit Leuven, Rutgers Universi- ty, and the Ludwig-Maximilians-Universitat Munchen and out of lectures I gave at the workshop "Hydrodynamical Behavior of Microscopic Systems" at the Universita dell'Aquila. I had the good luck of being helped through difficult ground by many friends. Amongst them I am deeply indebted to Joel L. Lebowitz. He got me started. Relatively little would have been achieved without his never-ending curiosity and insistence on clarity. Furthermore, I gratefully acknowledge the cooperation of Michael Aizenman, Henk van Beijeren, Carlo Boldrighini, Jean Bricmont, Paola Calderoni, Brian Davies, Anna DeMasi, Roland Dobrushin, Detlef Durr, Gregory Eyink, Mark Fannes, Pablo Ferrari, Alberto Frigerio, Joseph Fritz, Antonio Galves, Shelly Goldstein, Vittorio Gorini, Reinhard Illner, Claude Kipnis, Joachim Krug, Oscar Lanford, Reinhard Lang, Joel Lebowitz, Christian Maes, Stefano Olla, George Papanicolaou, Errico Presutti, Mario Pulvirenti, Fraydoun Rezakhanlou, Hermann Rost, Yasha Sinai, Yuri Suhov, Domo Szasz, Ragu Varadhan, Andre Verbeure, David Wick, and Horng-Tzer Yau. The list is somewhat lengthy, perhaps, but besides thanks I want to make clear that what I will describe is the outcome of a common scientific enterprise. I thank Henk van Beijeren and Detlef Durr for careful reading of and com- ments on a previous version. Paola Calderoni and Detlef Durr supplied me with the proof in Part I, Chapter 8. 4 which is most appreciated. Munchen, May 1991 Herbert Spohn Contents Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Scales . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .