  Semigroups describing the time evolution of open quantum systems in
finite-dimensional spaces have generators of a special form, known as Lindblad
generators. These generators and the corresponding processes of time evolution
are analyzed, characterized as Decay, Dissipation and Dephasing. In relation to
these processes the Hilbert space of the system is equipped with a special
structure, a decomposition into a sum of mutually orthogonal subspaces. The
complete set of all the stationary states and the asymptotic behavior of the
evolutions are presented in detail. Some unusual special facts about invariant
operators and symmetries are studied, examples are demonstrated. Perturbation
theory for the structure and for the stationary states is discussed and
performed in case studies.
