  The aim of these notes is to introduce the quantum master equation
$\{S,S\}-2i\hbar\Delta S=0$, and to show its relations to the theory of Lie
algebras representations and to perturbative expansions of Gaussian integrals.
The relations of the classical master equation $\{S,S\}=0$ with the BRST
formalisms are also described. Being an introduction, only finite-dimensional
examples will be considered.
