This text developed from materials the author has used in a one-semester course on elementary statistical mechanics. It assumes readers have had courses in calculus and physical chemistry. Its purpose is not only to give students a deeper understanding of thermodynamics and the principles of equilibrium statistical mechanics, but also to introduce them to the modern topics of Monte Carlo sampling, renormalization group theory, and the fluctuation-dissipation theorem. By frequent use of simplified models, the author has kept the mathematics in the text relatively simple while presenting many of the sophisticated ideas in the field. His approach is to deal first with macroscopic thermodynamics, then with microscopic statistical principles. The Second Law of Thermodynamics appears as the direct consequence of the statistical assumption that microscopic equilibrium is the state of greatest randomness. The different ensembles and the role of fluctuations are treated before non-interacting ideal systems and phase transformations are discussed. The treatment of phase transitions relies on the Ising model, which is also used to explain the Monte Carlo method. The last two chapters deal with equilibrium statistical mechanics of classical fluids and with dynamics, that is, relaxation an molecular motion in macroscopic systems which are at or close to equilibrium. This is a forward-looking text suitable for use by advanced undergraduate or beginning graduate students of chemistry, biochemistry, chemical engineering and physics.