  The dynamical mean-field theory (DMFT) is a widely applicable approximation
scheme for the investigation of correlated quantum many-particle systems on a
lattice, e.g., electrons in solids and cold atoms in optical lattices. In
particular, the combination of the DMFT with conventional methods for the
calculation of electronic band structures has led to a powerful numerical
approach which allows one to explore the properties of correlated materials. In
this introductory article we discuss the foundations of the DMFT, derive the
underlying self-consistency equations, and present several applications which
have provided important insights into the properties of correlated matter.
