Foundations of Statistical Mechanics

This revised and expanded second edition presents an accessible yet rigorous introduction to Statistical Physics and complex dynamical systems. The book is organized in two parts: the first (Chapters 1-7) covers classical foundations such as ensembles, gases, and probability distributions; the second (Chapters 8-14) develops nonlinear dynamics, including Brownian motion, dissipative maps, billiards, and spin models. Phase transitions are analyzed through scaling laws, critical exponents, and order parameters, with emphasis on both conservative and dissipative systems. The edition features more figures, exercises, and computational simulations to illustrate key concepts. Inspired by classic texts by Reif and Salinas, and enriched by recent research recognized with the 2023 Afraimovich Award, this work bridges traditional Statistical Physics with current advances in nonequilibrium phenomena. It is intended for undergraduate and graduate students interested in the physics of complex systems.