2014 Reprint of 1949 Edition. Full facsimile of the original edition, not reproduced with Optical Recognition Software. The translation of this important work brings to the American mathematician and physicist a useful work of statistical mechanics. It offers a precise and mathematically satisfactory formulation of the problems of statistical mechanics and provides the analytic tools needed to replace many of the cumbersome concepts and devices commonly found in more basic works on the subject. And above all, it furnishes the mathematician approaching the subject for the first time with a logical, step-by-step introduction, written in mathematical terms, to aid in mastering the subject in the shortest possible time. Contents Include: Geometry and kinematics of the phase space. -- Ergodic problem. -- Reduction to the problem of the theory of probability. -- Application of the central limit theorem. -- Ideal monatomic gas. -- The foundation of thermodynamics. -- Dispersion and the distributions of sum functions. Aleksandr Khinchin was a Soviet mathematician and one of the most significant people in the Soviet school of probability theory.