  The scope of this work is to provide a self-contained introduction to a
selection of basic theoretical aspects in the modeling and control of quantum
mechanical systems, as well as a brief survey on the main approaches to control
synthesis. While part of the existing theory, especially in the open-loop
setting, stems directly from classical control theory (most notably geometric
control and optimal control), a number of tools specifically tailored for
quantum systems have been developed since the 1980s, in order to take into
account their distinctive features: the probabilistic nature of atomic-scale
physical systems, the effect of dissipation and the irreversible character of
the measurements have all proved to be critical in feedback-design problems.
The relevant dynamical models for both closed and open quantum systems are
presented, along with the main results on their controllability and stability.
A brief review of several currently available control design methods is meant
to provide the interested reader with a roadmap for further studies.
