This book deals with one of the fundamental problems of nonequilibrium statistical mechanics: the derivation of large scale dynamics from microscopic models consisting of a very large number of interacting particles. In this monograph the author treats various macroscopic equations, in particular the Boltzmann equation for a low density fluid of hard spheres and the nonlinear diffusion equation for stochastic lattice gases. Also discussed are Gaussian fluctuations around the large scale deterministic motion, and the dynamics of tracer particles. The book addresses both researchers and students. Much of the material is presented here for the first time in book form.