  Ab initio calculation of the electronic properties of materials is a major
challenge for solid state theory. Whereas the experience of forty years has
proven density functional theory (DFT) in a suitable, e.g. local approximation
(LDA) to give a satisfactory description in case electronic correlations are
weak, materials with strongly correlated, say d- or f-electrons remain a
challenge. Such materials often exhibit colossal responses to small changes of
external parameters such as pressure, temperature, and magnetic field, and are
therefore most interesting for technical applications.
  Encouraged by the success of dynamical mean field theory (DMFT) in dealing
with model Hamiltonians for strongly correlated electron systems, physicists
from the bandstructure and many-body communities have joined forces and have
developed a combined LDA+DMFT method for treating materials with strongly
correlated electrons ab initio. As a function of increasing Coulomb
correlations, this new approach yields a weakly correlated metal, a strongly
correlated metal, or a Mott insulator.
  In this paper, we introduce the LDA+DMFT by means of an example, LaMnO_3 .
Results for this material, including the colossal magnetoresistance of doped
manganites are presented. We also discuss advantages and disadvantages of the
LDA+DMFT approach.
