An introduction to the Batalin-Vilkovisky formalism

The aim of these notes is to introduce the quantum master equation $\{S,S\}-2i\mathrm{\hslash }\mathrm{\Delta }S=0$, 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.