The initial intention was to prepare a review article which covers the latest progress in a variety of physical fields dealing with non-equilibrium many-body systems. During the last decade, kinetic theories developed within the chemical, nuclear, plasma and solid-state physics have started to merge whereas previously they were based on rather distinct approaches. It turned out that to cover all essential concepts on a basis of a unified theory exceeds the frame of a review article. We have been encouraged by a community of theoretical physicists to extend the manuscript into a monograph.

The manuscript is aimed for a wide audience of theoretical physicists interested in non-equilibrium many body systems. Selected chapters can be studied by advanced undergraduate students. Advanced chapters (denoted by stars) are addressed to a growing community of physicists having at least rudimentary knowledge of Green's functions. We expect particular interest from physicists involved in nuclear matter only for which field we give applications as not to drive reader's attention into many directions. For non-experts in nuclear matter, we first review properties of nuclear matter which are discussed in the light of experience from other fields.

All steps of the derivation from non-equilibrium quantum statistics are introduced in their historical background, from the simplest approximations to their recent form. The text is structured so that a reader not interested in technical details can follow selected chapters. In this case, the reader will approach the theory from the quasiclassical picture and learn how to implement it in practise.