This book describes the main ideas and methods that underlie the application of statistical mechanics to a wide variety of fields in science. It has a greater emphasis on the links between the basic microscopic laws of classical and quantum physics and statistical mechanics than can be found in other texts at the same level. The book is organised into three parts. The first section recounts basic lines of argument leading from microscopic description to the standard equilibrium ensembles in classical mechanics and quantum mechanics. The second section describes applications of the equilibrium ensembles to systems of progressively increasing density: ideal gases, imperfect gases (cluster expansions), liquids, and solids, and finally phase transitions and the renormalization group for the study of critical points. The final section deals with dynamics, including a careful account of the meaning of hydrodynamic theories in microscopic terms and linear response theory.