Thermodynamics.
Equilibrium states, thermodynamics, state functions, zeroth law. First principle. Equation of state of a perfect gas. Response functions. Second principle (Clausius), Carnot's theorem and entropy. Relationship between response functions. Stability of equilibrium states, thermodynamic potentials and their convexity properties. Maxwell's relations. The third law. Thermodynamic description of phase transitions. The coexistence curve and Clausius Clapeyron equation. Van der Waals equation of state, critical point and the law of corresponding States. Maxwell construction. Critical exponents and their value for the case of Van der Waals. Landau theories, evaluation of critical exponents.

Fundamentals of statistical mechanics.
Fundamentals of classical statistical mechanics, Gibbs ensembles. Microcanonical ensemble formalism. The ideal gas. Gibbs paradox and the Boltzmann factor. Equipartition theorem. The canonical formulation. Equivalence of ensembles. Model for the Van der Waals equation. Grand canonical ensemble and equivalence with the canonical ensemble. Langmuir adsorption isotherm. Existence of the thermodynamic limit for Van Hove potentials. Cluster and virial expansions. Second virial coefficient for simple potentials. Density matrices in quantum mechanics, identical particles systems, quantum Gibbs ensembles. Classical limit of quantum partition function.

Perfect quantum gases.
Bose gases: crystal lattice in Debye approximation, specific heat at low and high temperatures. Bose-Einstein condensation: the population of the state of minimum energy, interpretation as first order phase transition. Degenerate Fermi Gas, Fermi energy and chemical potential, specific heat at low temperatures. Pauli paramagnetism and Landau diamagnetism.