Electronic excitations in metals. Electron-phonon interaction. Frohlich hamiltonian. Cooper problem. BCS theory. Unconventional superconductivity. Bogolubov transformation. Excitation spectrum. Selfconsistency equation. Thermodynamics of superconductors. Landau expansion of the free energy close to the critical temperature. Nonuniform superconducting state. Bogolubov equations. Andreev equations. Andreev reflection. Andreev bound states in vortex cores, near interfaces. Josephson effect in SIS and SNS heterostructures. Green's function approach to the theory of superconductivity. Gor'kov equations. Ginzburg-Landau theory. Linear response of the superconductor to magnetic field. Meissner effect. Magnetic penetration depth in unconventional superconductors. Effect of impurities on superconducting state. Anderson's theorem. Magnetic impurities. Gapless superconductivity. Impurity-induced bound states. Quasiclassical theory of superconductivity. Eilenberger equations. Usadel equations. Mixed and vortex state. Surface superconductivity. Nonequilibrium superconductivity.