  A number of methods are discussed which may serve for a treatment of electron
correlations in solids. When the electron correlations are relatively weak like
in semiconductors or a number of ionic crystals one may start from a
self-consistent field calculation and include correlations by quantum chemical
methods. An incremental computational scheme enables us to obtain results of
high quality for the ground state of those systems. A number of examples
demonstrates that explicitely.
  Solids with strongly correlated electrons require the use of model
Hamiltonians. With their help one can tackle the problem of determining
spectral densities for those systems. The projection technique is a useful tool
here. In strongly correlated $f$ electron systems electron or holes can
crystallize with quite different physical consequences as in the case of a
Wigner crystal or Verwey transition. Finally, different routes to heavy-fermion
behavior are discussed, another hallmark of strongly correlated electrons.
