This volume contains the text of four sets of lecturesdelivered at the third session of the Summer School
organized by C.I.M.E. (Centro Internazionale Matematico
Estivo). These texts are preceded by an introduction written
by C. Cercignani and M. Pulvirenti which summarizes the
present status in the area of Nonequilibrium Problems in
Many-Particle Systems and tries to put the contents of the
different sets of lectures in the right perspective, in
order to orient the reader. The lectures deal with the
global existence of weak solutions for kinetic models and
related topics, the basic concepts of non-standard analysis
and their application to gas kinetics, the kinetic equations
for semiconductors and the entropy methods in the study of
hydrodynamic 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.

Nonequilibrium problems in many-particle systems. An introduction.- Some examples of NSA methods in kinetic theory.- Global solutions of kinetic models and related questions.- Kinetic models for semiconductors.- Entropy methods in hydrodynamic scaling.