Elements of Non-equilibrium Statistical Mechanics: random walk, Markov process, Brownian motion, Langevin equation, Fokker-Planck equation, Boltzmann equation, H-theorem and irreversibility, linearized Boltzmann equation, collision integral, relaxation time approximation, irreversibility and approach to the equilibrium; Statistical Fields: collective behavior, phonon and elasticity, from bits to fields, continuum limit, Hubbard-Stratonovich transformation, Landau-Ginzburg Hamiltonian, saddle point approximation, mean field theory, continuous symmetry breaking, Goldstone modes, discrete symmetry breaking, domain walls; Fluctuations: scattering and fluctuation, correlation functions and susceptibilities, lower critical dimension, gaussian integrals, fluctuation corrections to the saddle point, Ginzburg criterion; Phase Transitions and Critical Phenomena: phase, phase diagram, phase transition, critical phenomena, scale transformation, meanfield approximation, critical exponents, Landau theory, variational method, Bethe approximation, correlation function; Renormalization Group And Scaling: coarse graining and scale transformation, parameter space, renormalization group equation, scaling law, anomalous dimensions; Perturbative Renormalization Group: critical Hamiltonian, Feynman diagram, fixed point and critical behavior, models with O(N) symmetry, renormalization group near dimension 4, renormalization group for N-components fields, gradient flow; Conformal Field Theory: introduction, conformal invariance, quasi-primary fields, Ward identity, central charge, Virasoro algebra, representation theory, Hamiltonian on a cylinder, Thermodynamic Bethe ansatz.