Learn advanced concepts in Statistical Mechanics through this graduate-level lecture from IMPA's 2025 Summer School, delivered in Portuguese by Professor Hubert Lacoin. Explore fundamental topics including Hamiltonian systems, Liouville's theorem, Poincaré recurrence theorem, Birkhoff's theorem, Boltzmann hypothesis, statistical ensembles, Gibbs measure, Ising model, thermodynamic limit, FKG inequality, phase transitions, phase diagrams, FK models, and Pirogov-Sinai theory. Drawing from key references like Feynman's Statistical Mechanics lectures, Presutti's work on scaling limits, and specialized texts on the Ising model, gain a comprehensive understanding of statistical mechanical principles and their mathematical foundations. Note that while this lecture is part of a master's program curriculum, doctoral students may have additional requirements.