This critical analysis of the foundations of statistical mechanics based on Boltzmann's work emphasizes the relationship between microscopic reversibility and macroscopic irreversibility. It discusses the theory of ensembles and phase-transition phenomena in simple models. The book also includes some very modern development, such as the theory of nonequilibrium ensembles based on Ruelle's principle and dynamical theories related to the Ruelle-Takens theory of turbulence. It also treats ergodicity, entropy, equipartition, and the limits of Brownian motion.