  A common theme in mathematics is the evaluation of Gauss integrals. This,
coupled with the fact that they are used in different branches of science,
makes the topic always actual and interesting. In these notes we shall analyze
a particular class of Gaussian integrals that depends by the quantum parameter
$\hbar$. Starting from classical results, we will present an overview on
methods, examples and analogies regarding the practice of solving quantum
Gaussian integrals.
