This text distills the core ideas of statistical mechanics to make room for new advances important to information theory, complexity, active matter, and dynamical systems. Chapters address random walks, equilibrium systems, entropy, free energies, quantum systems, calculation and computation, order parameters and topological defects, correlations and linear response theory, and abrupt and continuous phase transitions. Exercises explore the enormous range of phenomena where statistical mechanics provides essential insight — from card shuffling to how cells avoid errors when copying DNA, from the arrow of time to animal flocking behavior, from the onset of chaos to fingerprints. The text is aimed at graduates, undergraduates, and researchers in mathematics, computer science, engineering, biology, and the social sciences as well as to physicists, chemists, and astrophysicists. As such, it focuses on those issues common to all of these fields, background in quantum mechanics, thermodynamics, and advanced physics should not be needed, although scientific sophistication and interest will be important.