Kinetic theory is defined as a branch of statistical mechanics that attempts to describethe non-equilibrium properties of macroscopic systems in terms of microscopic propertiesof the constituent particles or quantum excitations. The history of kinetic theory is summarizedfrom the first understandings of the connections of temperature and pressure ofperfect gases with their average kinetic energy and with the average momentum transferto the walls by particle-wall collisions. The history continues with a discussion of the contributionsof Maxwell and Boltzmann, and the development of the Boltzmann transportequation. Modern developments include extending the Boltzmann equation to moderatelydense gases, formulation of kinetic theory for hard sphere systems, discovery of long timetail contributions to the Green-Kubo expressions for transport coefficients, applications ofkinetic theory to fluctuations in gases, to quantum gases and to granular particles. Thecontents of each chapter are then summarized.

Boltzmann’s transport equation for a dilute gas with particles interacting with central, short range forces, and with bounding walls, is derived in detail, with emphasis on the use of the Stosszahlansatz. Boltzmann’s H–theorem is presented as a microscopic derivation of the law of entropy increase in non–equilibrium processes, and the Maxwell–Boltzmann equilibrium distribution is derived. Zermelo’s and Loschmidt’s arguments that the H–theorem is incompatible with the laws of mechanics are given and discussed. The Kac ring model is presented and used as a simple way to understand the application and the limitations of the Stosszahlansatz. It is concluded that the Boltzmann equation is statistical, rather than strictly mechanical, in nature, providing a description of the most probable non–equilibrium behavior of a dilute gas.