1 Basic Concepts. - 1. 1 Introduction: Whys and Hows of Quantum Many-Body Theory. - 1. 2 Propagation Function in a One-Body Quantum Theory. - 1. 3 Perturbation Theory for the Propagator. - 1. 4 Second Quantization. - 1. 5 Problems to Chapter 1. - 2 Green's Functions at Zero Temperature. - 2. 1 Green's Function of The Many-Body System: Definition and Properties. - 2. 2 Perturbation Theory: Feynman Diagrams. - 2. 3 Problems to Chapter 2. - 3 More Green's Functions Equilibrium and Otherwise and Their Applications. - 3. 1 Analytic Properties of Equilibrium Green's Functions. - 3. 2 Matsubara formalism. - 3. 3 Linear Response Theory. - 3. 4 Nonequilibrium Green's Functions. - 3. 5 Quantum Kinetic Equation. - 3. 6 Application: Electrical Conductivity of Quantum Point Contacts. - 3. 7 Method of Tunneling Hamiltonian. - 3. 8 Problems to Chapter 3. - 4 Methods of the Many-Body Theory in Superconductivity. - 4. 1 Introduction: General Picture of the Superconducting State. - 4. 2 Instability of the Normal State. - 4. 3 Pairing (BCS) Hamiltonian. - 4. 4 Green's Functions of a Superconductor: The NambuGor'kov Formalism. - 4. 5 Andreev Reflection. - 4. 6 Tunneling of Single Electrons and Cooper Pairs. - 4. 7 Problems to Chapter 4. - A Landauer Formalism for Hybrid Normal-Superconducting. - Structures. - A. 1 The LandauerLambert formula. - A. 2 Giant Conductance Oscillations in Ballistic Andreev Interferometers. - References. Language: English