Review of Thermodynamics: laws of thermodynamics, postulates of equilibrium thermodynamics, intensive parameter of thermodynamics, equilibrium, Euler and Gibbs-Duhem relations, thermodynamic potential, Maxwell relations, variational principle; Kinetic Theory of Gas: general definitions, Liouville’s theorem, BBGKY hierarchy, Boltzmann equation, H-theorem and irreversibility, equilibrium properties, Maxwell-Boltzmann distribution, conservation laws, hydrodynamics; Microcanonical Ensemble: postulates of classical statistical mechanics, the definition of the microcanonical ensemble, thermodynamics, equipartition theorem, classical ideal gas, Gibbs paradox; Canonical Ensemble: equilibrium between a system and a heat reservoir, definition of canonical ensemble, partition function, various statistical quantities, classical systems, energy fluctuation, equipartition and viral theorem, harmonic oscillator, paramagnetism; Grand Canonical Ensemble: equilibrium between a system and a particle–energy reservoir, chemical potential, definition of grand canonical ensemble, various statistical quantities, density and energy fluctuation, phase diagram, Clausius-Clapeyron equation; Quantum Statistical Mechanics: postulates of quantum statistical mechanics, density matrix, and ensembles in quantum statistical mechanics, the third law of thermodynamics, ideal gases: microcanonical and canonical ensemble; Ideal Bose System: thermodynamic behavior, Bose-Einstein statistics, photon, thermodynamics of the blackbody radiation, phonon in solid, Bose-Einstein condensation; Ideal Fermi System: thermodynamic and magnetic behavior of an ideal Fermi gas, Fermi-Dirac statistics, electron gas in metals, Landau diamagnetism, Pauli paramagnetism, ultracold Fermi gas, statistical equilibrium of white dwarf stars; Properties of Partition Function: DarwinFowler method, classical limit, singularities and phase transition, Lee-Yang circle theorem, cumulant expansion, cluster expansion, second viral coefficient and van der Walls equation, mean field theory, variational methods; The Ising Model: definition, equivalence to other models, spontaneous magnetization, Bragg-Williams approximation, Bethe-Peierls approximation, 2-dimensional Ising model, the Onsager solution; Critical Phenomena: order parameter, correlation function, fluctuation-dissipation theorem, critical exponents, scaling hypothesis, scale invariance, Goldstone excitation, dimensionality, Landau free energy, mean-field theory, tricritical point, Gaussian model, Ginzburg criterion, anomalous dimension; Renormalization Group: block spins, one-dimensional Ising model, renormalization group transformation, fixed point and scaling of fields, momentum space formulation, Gaussian model, Landau-Wilson model.