General idea of phase transitions. Magnetic systems. Critical point in fluid. Medium field theory. Critical indices in the medium field theory. Magnetics with an infinite radius of interaction. The theory of van der Waals for the transition liquid-gas as a medium field theory. Landau theory of phase transitions of the second order. Order parameter, symmetry, fluctuations near the critical point, correlation length. Ginzburg criterion. Influence of external field on phase transition. One-dimensional Ising model. Exact solution, behavior of correlation length at low temperatures, role of topological defects in destruction of long-range order. Construction of high-temperature expansions for one- and two-dimensional Ising model. Analysis of the radius of convergence of series. Pad? approximant. Evaluation of critical indices from high-temperature expansions. Two-dimensional Ising model. Duality, Onsager's solution. Method of transfer-matrix in two-dimensional Ising model. Effective one-dimensional Hamiltonian and description of critical behavior in terms of massless fermions. Scale invariance. Renormalization group in real space for one- and two-dimensional Ising model. Fixed points and critical indices. Calculation of critical indices in the e-expansion. Peculiarity of renormalization group transformations near dimension d = 4. Gaussian fixed point. Fixed point at d <4. Index of correlation length in the lowest approximation to e. Phase transitions in magnetics near d = 2. Derivation of renormalization group equations of Polyakov and temperature of transition at d = 2 + e. Two-dimensional XY-model. Spin correlator in Gaussian approximation. Vortices, interaction of vortices. Berezinsky–Kosterlitz–Thouless transition. Equations of Kosterlitz renormalization group. Behavior of correlation length near transition point. Gas of particles with logarithmic potential and Kosterlitz–Thouless transition in other models (the Ising model with long-range interaction, instantons under tunneling with friction). Percolation theory. Percolation threshold, hypothesis of scaling and critical indices. Fractal dimension of clusters. Renormalization group transformation for one-dimensional problem and for triangular lattice in two dimensions. Introduction to SLE. Levner equation, his solution in the simplest cases. Relationship between diffusion coefficient and fractal dimension of critical curves. Application to percolation theory. Dynamics of systems near phase transition point. Attenuation in critical region. Glauber dynamics and relaxation in one-dimensional Ising model. Self-organized criticality. Model of sand hill in one and two dimensions. Dynamics of avalanches.