This graduate textbook covers contemporary directions of non-equilibrium statistical mechanics as well as classical methods of kinetics. Starting from phenomenological non-equilibrium thermodynamics, the kinetic equation method discussed and demonstrated with electrons and phonons in conducting crystals. Linear response theory as well as the non-equilibrium statistical operator and the master equation approach are discussed in the course of the book. With one of the main propositions being to avoid terms such as "obviously" and "it is easy to show", this treatise is an easy-to-read introduction into this traditional, yet vibrant field. Problems and their well-documented solutions included at appropriate points of the narrative allow the reader to actively develop essential parts of the theory himself. From the content: Phenomenological thermodynamics of irreversible processes Brownian motion Kinetic equations in non-equilibrium thermodynamics Kinetic equation for electrons and phonons in conducting crystals Theory of non-linear response to an external mechanical pertubation Non-equilibrium statistical operator method Response of a highly non-equilibrium system to a weakly measuring field Master equation approachweiterlesen