Main topics:

Second quantization.
    Fock space. Creation and annihilation operators and field operators. Operators in second     quantization.

Landau theory of normal Fermi liquids.
    Introduction to the concept of quasi-particle. Energy as a functional of the quasi-particle         distribution function. Equilibrium properties of quasi-particles: effective mass, specific             heat, compressibility, spin suceptibility. Stability of the ground state. Currents associated     to the quasi-particles. Kinetic equations: collective modes and zero-sound.

Green function and perturbation techniques.
    Single-particle Green function at T=0. Spectral representation and poles. Equation of             motion. Interaction representation. S matrix. Wick's theorem and Feynman diagrams.            Diagrammatic rules for different interction types. Self-energy and Dyson equation.                 Hartree-Fock approximation, RPA.
    Perturbation theory at T>0. Matsubara Green function. Perturbation techniques and             thermodynamic potential.
    Identification of the phenomenological parameters of Landau's theory with microscopic         quantities. Quasi-particle lifetime.

Linear response theory.
    Response function. Analytic properties. Reactive and absorptive part. Kramers-Kronig         relations. Kubo formula    Fluctuation and dissipation theorem. Spectral representation         and sum rules. Conductivity. Continuity equation and gauge invariance. Esplicit                     calculation of response functions in perturbation theory (RPA) in simple cases of physical     interest.