Statistical mechanics : a concise advanced textbook / Sergio Cecotti.

Includes bibliographical references and index.

Thermodynamical formalism -- Equilibrium ensembles -- Non-interacting quantum systems -- Phase transitions and lattice systems -- Approximate methods and Landau theory -- Linear response theory and Brownian motion -- Frustrated and quenched systems.

This advanced textbook offers a mathematically rigorous and self-contained introduction to statistical mechanics for upper-level undergraduate and graduate students in physics and mathematics. Based on lecture notes developed for highly talented students at Qiuzhen College, Tsinghua University, the book systematically explains the foundations of thermodynamics, equilibrium ensembles, quantum statistical systems, phase transitions, lattice models, and stochastic processes. The text emphasizes both physical intuition and mathematical precision, carefully distinguishing rigorous derivations from controlled approximations. In addition to standard topics, the work introduces advanced concepts such as Yang-Lee theory, order-disorder duality, fluctuation-dissipation relations, spin glasses, Brownian motion, supersymmetry in stochastic equations, and path integral methods. Through detailed discussions, examples, and theoretical insights, the book serves as an important resource for students, researchers, and professionals interested in modern statistical physics and mathematical physics.