This book is an introduction to statistical mechanics and thermodynamics. Relevant probability theory is included. Part 1 develops the basic ideas of statistical mechanics, as illustrated by a complete derivation of the entropy of the classical ideal gas based on Boltzmann's 1877 definition. This leads to a systematic development of thermodynamics in Part 2. Part 3 is devoted to classical statistical mechanics, including a discussion of irreversibility. Part 4 covers quantum statistical mechanics, including lattice vibrations, black-body radiation, Bose-Einstein statistics, Fermi-Dirac statistics, and the Ising model of phase transitions. The text presents many problems that support conceptual development, with a strong emphasis on computational methods. A manual with complete solutions to all problems is available to instructors.