  In Batalin-Vilkovisky formalism a classical mechanical system is specified by
means of a solution to the {\sl classical master equation}. Geometrically such
a solution can be considered as a $QP$-manifold, i.e. a super\m equipped with
an odd vector field $Q$ obeying $\{Q,Q\}=0$ and with $Q$-invariant odd
symplectic structure. We study geometry of $QP$-manifolds. In particular, we
describe some construction of $QP$-manifolds and prove a classification theorem
(under certain conditions).
  We apply these geometric constructions to obtain in natural way the action
functionals of two-dimensional topological sigma-models and to show that the
Chern-Simons theory in BV-formalism arises as a sigma-model with target space
$\Pi {\cal G}$. (Here ${\cal G}$ stands for a Lie algebra and $\Pi$ denotes
parity inversion.)
