  These lecture notes address an audience of physicists or mathematicians who
have been exposed to a first course in quantum mechanics. We start with a brief
discussion of the general "system-bath" paradigm of quantum dissipative
systems, analyze in some detail the simplest example of "pure dephasing" of a
two-level system, and review the basic concept of the density matrix. We then
treat the general dissipative time-evolution, introducing completely positive
maps, their relation to entanglement theory, and their Kraus decomposition.
Restricting ourselves to Markovian evolution, we discuss the Lindblad form of
master equations. The notes conclude with an overview of topics of current
interest that go beyond Lindblad Markov master equations. (These notes were
prepared for lectures delivered by F. Marquardt in October 2007 at the Langeoog
workshop of the SFB/TR 12, "Symmetries and Universality in Mesoscopic Systems")
