Dirac notation; Transformation theory; Second quantization; Particle creation and annihilation operators; Schrodinger, Heisenberg and
Interaction Pictures; Linear response; S-matrix; Density matrix; Superoperators and non-Markovian kinetic equations; Schwinger Action Principle and variational calculus; Quantum Hamilton equations; Field equations with particle sources, potential and phonon sources; Retarded Green's functions; Localized state in continuumand chemisorption; Dyson equation; T-matrix; Impurity scattering; Self-consistent Born approximation;Density-of-states;Greens function matching; Ensemble averages and statistical thermodynamics, Bose and Fermi distributions, Bose condensation; Thermodynamic Green's functions; Lehmann spectral representation; periodicity/antipeiodicity in imaginary time and Matsubara Fourier series/frequencies; Anallytic continuation to real time;
 Multiparticle Green's functions; Electromagnetic current-current correlation  response; Exact variational relations for multiparticle
Green's functions; Cumulants; Linked cluster theorem; Random phase
approximation; Perturbation  theory for green's functions, self-energy and vertex functions by variational differential formulation; Shielded potential perturbation theory;Imaginary time contour ordering Langreth algebra and the GKB Ansatz.
        

Typical texts: Kadanoff and Baym, Quantum Statistical
Mechanics, and Inkson, Many-Body Theory of Solids.