This volume contains the text of four sets of lecturesdelivered at the third session of the Summer Schoolorganized by C.I.M.E. (Centro Internazionale Matematico Estivo). These texts are preceded by an introduction writtenby C. Cercignani and M. Pulvirenti which summarizes thepresent status in the area of Nonequilibrium Problems in Many-Particle Systems and tries to put the contents of thedifferent sets of lectures in the right perspective, inorder to orient the reader. The lectures deal with theglobal existence of weak solutions for kinetic models andrelated topics, the basic concepts of non-standard analysisand their application to gas kinetics, the kinetic equationsfor semiconductors and the entropy methods in the study ofhydrodynamic limits. CONTENTS: C. Cercignani, M. Pulvirenti: Nonequilibrium Problems in Many-Particle Systems. An Introduction.- L. Arkeryd: Some Examples of NSA in Kinetic Theory.- P.L. Lions: Global Solutions of Kinetic Models and Related Problems.- P.A. Markowich: Kinetic Models for Semiconductors.- S.R.S. Varadhan: Entropy Methods in Hydrodynamic Scaling.