Gibbs' ensemble theory develops consistent non-equilibrium statistical mechanics. It is based on the idea of weak limits of solutions of the Liouville equation with an unlimited increase in time. With its help, the problem of transition to macrodescription is naturally solved, when the main focus is on the study of the evolution of average values (mathematical expectations) of dynamic quantities. This approach differs from traditional approaches to the problem of irreversibility, since the equilibrium states of dynamical systems in the past and in the future coincide. General results are applied to the solution of specific problems of classical statistical mechanics. The book is intended for mathematicians, mechanics and physicists interested in statistical mechanics and questions of substantiation of thermodynamics.