  The concept of electronic correlations plays an important role in modern
condensed matter physics. It refers to interaction effects which cannot be
explained within a static mean-field picture as provided by Hartree-Fock
theory. Electronic correlations can have a very strong influence on the
properties of materials. For example, they may turn a metal into an insulator
(Mott-Hubbard metal-insulator transition). In these lecture notes I (i)
introduce basic notions of the physics of correlated electronic systems, (ii)
discuss the construction of mean-field theories by taking the limit of high
lattice dimensions, (iii) explain the simplifications of the many-body
perturbation theory in this limit which provide the basis for the formulation
of a comprehensive mean-field theory for correlated fermions, the dynamical
mean-field theory (DMFT), (v) derive the DMFT self-consistency equations, and
(vi) apply the DMFT to investigate electronic correlations in models and
materials.
