  These notes are intended to provide a self-contained introduction to the
basic ideas of finite dimensional Batalin-Vilkovisky (BV) formalism and its
applications. A brief exposition of super- and graded geometries is also given.
The BV-formalism is introduced through an odd Fourier transform and the
algebraic aspects of integration theory are stressed. As a main application we
consider the perturbation theory for certain finite dimensional integrals
within BV-formalism. As an illustration we present a proof of the isomorphism
between the graph complex and the Chevalley-Eilenberg complex of formal
Hamiltonian vectors fields. We briefly discuss how these ideas can be extended
to the infinite dimensional setting. These notes should be accessible to both
physicists and mathematicians.
