Statistical mechanics is a fundamental part of theoretical physics. Not only does it provide the basic tools for analyzing the behavior of complex systems in thermal equilibrium, but also hints at, and is fully compatible with, quantum mechanics as the theory underlying the laws of nature. In the process one encounters such complex emergent phenomena as phase transitions, superfluidity, and superconductivity which are highly non-trivial consequences of the microscopic dynamics. At the same time statistical mechanics poses conceptual problems such as how irreversibilty can appear from an underlying microscopic system governed by reversible laws.

Historically, statistical mechanics grew out of classical thermodynamics with the aim of providing a dynamical foundation for this phenomenological theory. It thus deals with many-body problems starting from a microscopic model which is typically described by a simple Hamiltonian. The power of statistical mechanics lies in both its simplicity and universality. Indeed the same concept can be applied to a wide variety of systems both classical and quantum mechanical. These include non-interacting and interacting gases, chemical interactions, paramagnetic and spin systems, astrophysics, and solids. On the other hand statistical mechanics brings together a variety of different tools and methods used in theoretical physics, chemistry, and mathematics. Indeed while the basic concepts are easily explained in simple terms a quantitative analysis will quickly involve sophisticated methods.

The purpose of this book is twofold: to provide a concise and self-contained introduction to the key concepts of statistical mechanics and to present the important results from a modern perspective. The book is introductory in character, and should be accessible to advanced undergraduate and graduate students in physics, chemistry, and mathematics.