  This manuscript is an edited and refined version of the lecture script for a
one-semester graduate course given originally at the PhD school in the
Institute of Physics of Polish Academy of Sciences in the Spring/Summer
semester of 2022. The course expects from the student only a basic knowledge on
graduate-level quantum mechanics. The script itself is largely self-contained
and could be used as a textbook on the topic of open quantum systems. The
program of this course is based on a novel approach to the description of the
open system dynamics: It is showed how the environmental degrees of freedom
coupled to the system can be represented by a multi-component quasi-stochastic
process. Using this representation one constructs the super-quasi-cumulant (or
super-qumulant) expansion for the system's dynamical map -- a parametrization
that naturally lends itself for the development of a robust and practical
perturbation theory. Thus, even an experienced researcher might find this
manuscript of some interest.
