Contents -- Preface -- 1 Introduction -- 1.1 Quasiparticles and Green's functions -- 1.2 Diagram technique. Dyson equation -- 1.3 Green's functions at finite temperatures -- 2 Electron-Electron Interaction -- 2.1 Diagram rules -- 2.2 Electron gas with Coulomb interaction -- 2.3 Polarization operator of free electron gas at T = 0 -- 2.4 Dielectric function of an electron gas -- 2.5 Electron self-energy effective mass and damping of quasiparticles -- 2.6 RKKY-oscillations -- 2.7 Linear response -- 2.8 Microscopic foundations of Landau-Silin theory of Fermi-liquids -- 2.9 Interaction of quasiparticles in Fermi-liquid -- 2.10 Non-Fermi-liquid behavior -- 3 Electron-Phonon Interaction -- 3.1 Diagram rules -- 3.2 Electron self-energy -- 3.3 Migdal theorem -- 3.4 Self-energy and spectrum of phonons -- 3.5 Plasma model -- 3.6 Phonons and fluctuations -- 4 Electrons in Disordered Systems -- 4.1 Diagram technique for "impurity" scattering -- 4.2 Single-electron Green's function -- 4.3 Keldysh model -- 4.4 Conductivity and two-particle Green's function -- 4.5 Bethe-Salpeter equation "diffuson" and "Cooperon" -- 4.6 Quantum corrections self-consistent theory of localization and Anderson transition -- 4.6.1 Quantum corrections to conductivity -- 4.6.1.1 Technical details -- 4.6.1.2 "Poor man" interpretation of quantum corrections -- 4.6.2 Self-Consistent Theory of Localization -- 4.6.2.1 Metallic phase -- 4.6.2.2 Anderson insulator -- 4.6.2.3 Frequency dispersion of the generalized diffusion coefficient -- 4.7 "Triangular" vertex -- 4.8 The role of electron-electron interaction -- 5 Superconductivity -- 5.1 Cooper instability -- 5.2 Gorkov equations -- 5.3 Superconductivity in disordered metals -- 5.4 Ginzburg-Landau expansion -- 5.5 Superconductors in electromagnetic field.

6 Electronic Instabilities and Phase Transitions -- 6.1 Phonon spectrum instability -- 6.2 Peierls dielectric -- 6.3 Peierls dielectric with impurities -- 6.4 Ginzburg-Landau expansion for Peierls transition -- 6.5 Charge and spin density waves in multi-dimensional systems. Excitonic insulator -- 6.6 Pseudogap -- 6.6.1 Fluctuations of Peierls short-range order -- 6.6.2 Electron in a random field of fluctuations -- 6.6.3 Electromagnetic response -- 6.7 Tomonaga-Luttinger model and non Fermi-liquid behavior -- Appendix A Fermi Surface as Topological Object -- Appendix B Electron in a Random Field and Feynman Path Integrals -- Bibliography.