In this book an attempt is made to give a unified account of the present state of nonequilibrium statistical thermodynamics as a natural generalization of the equilibrium theory.From a logical point of view, it would be desirable to develop the statistical theory of nonequilibrium processes first, and treat the theory of statistical equilibrium as its limiting case. Such an approach, however, is scarcely worthwhile at the present time, since nonequilibrium and equilibrium statistical thermodynamics are at very different stages of development. In Chapters I and II, therefore, we give a brief account of the basic ideas of the classi­cal and quantum statistical mechanics of equilibrium systems, to the extent that this is necessary for the derivation of the basic thermodynamic relations for the case of statistical equilibrium.The purpose of these introductory chapters is to recall the general method of Gibbsian statistical ensembles, since later, in Chapters in and IV, attempts are made to take over the ideas of statistical ensembles to nonequilibrium statistical thermody­namics.