The problem of polaron. Perturbation theory. Feynman variational method. Superconductivity. BCS wave function. Perfect diamagnetism in the BCS model. Ginzburg-Landau theory. Vortex filaments, type II superconductors. One-dimensional fermions. Tomonagi model. Luttinger fluid. Many-boson systems. Trial wave functions of ground and excited states. Feynman formula for excitation spectrum in Bose-liquid. Two-dimensional superfluidity and superconductivity. Berezinsky–Kosterlitz–Thouless transition. Kondo effect. Perturbation theory. Renormalization group and exact solution. Anderson localization. Particle in a random potential. Diagram technique for disorder averages. Quantum correction to residual conductivity of disordered metal. Hopping conduction, Mott formula. Statistic of levels in complex systems. Gaussian ensembles of random matrices. The quantum Hall effect. Integer quantization of Hall conductivity. Hall conductivity as a topological invariant. Fractional quantization, Laflin wave function, quasi-particles with fractional charge. Effective action with Chern-Simons term. Mesoscopic physics. Phase coherence, undamped currents in rings. Tunneling contacts. Coulomb blockade. Destruction of coherence due to interaction with the environment. Can interaction of particles with each other destroy coherence?   LITERATURE R. Feynman Statistical mechanics. A.M. Tsvelik Quantum field theory in condensed matter physics.