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The science of statistical mechanics is concerned with defining the thermodynamic properties of a macroscopic sample in terms of the properties of the microscopic systems of which it is composed. The aim of this book is to provide a clear, logical, and self-contained treatment of equilibrium statistical mechanics starting from Boltzmann's two statistical assumptions, and to present a wide variety of applications to diverse physical assemblies. The coverage is enhanced and extended through an extensive set of accessible problems. It contains an appendix that provides an introduction to non-equilibrium statistical mechanics through the Boltzmann equation and its extensions. This book assumes introductory courses in classical and quantum mechanics, as well as familiarity with multi-variable calculus and the essentials of complex analysis. Some knowledge of thermodynamics is assumed, although the book starts with an appropriate review of that topic. The targeted audience is first-year graduate students, and advanced undergraduates, in physics, chemistry, and the related physical sciences. The goal of this text is to help the reader obtain a clear working knowledge of the very useful and powerful methods of equilibrium statistical mechanics and to enhance the understanding and appreciation of the more advanced texts.