  The main goal of these notes is to give an introduction to the mathematics of
quantum noise and some of its applications in non-equilibrium statistical
mechanics. We start with some reminders from the theory of classical stochastic
processes. We then provide a brief overview of quantum mechanics and quantum
field theory, from the viewpoint of quantum probability and adopting the
language of Hudson and Parthasarathy. We introduce quantum stochastic processes
on a boson Fock space and their calculus. Whenever possible, we make
connections with the relevant concepts in classical probability theory. As an
application of the theory, we introduce the theory of open quantum systems,
with emphasis on the physics and modeling aspects of these systems.
