Fifty years of kinetic theory

While the kinetic theory of dilute gases based on Boltzmann's 1872 equation was essentially completed by Chapman and Enskog around 1915, a concentrated effort to generalize the Boltzmann equation systematically to higher densities to obtain expansions of the transport coefficients in powers of the density was only started about 1945. Around 1965 it was realized, however, that this was impossible and that non-analytic terms in the density would occur. This ended the classical period of kinetic theory and inaugurated the modern era at about the same time as this occurred in the theory of phase transitions. New phenomena for which a kinetic, i.e., molecular, theory were given, include: the long time (tail) correlations in equilibrium time correlation functions related to the transport coefficients and later the long spatial correlations of density fluctuations in non-equilibrium stationary states. In addition a kinetic theory has been developed for the transport properties of dense gases and liquids. The theory is based on identifying the relevant collision processes as suggested by computer simulations of dense hard sphere fluids and by neutron scattering experiments of atomic liquids: ring and cage collisions. The theory has been applied to dense simple liquids as well as to concentrated colloidal suspensions. Finally, some open problems and current investigations are discussed.