  This paper is devoted to the construction and analysis of the Wigner
functions for noncommutative quantum mechanics, their marginal distributions
and star-products, following a technique developed earlier, {\it viz\/,} using
the unitary irreducible representations of the group $\g$, which is the three
fold central extension of the abelian group of $\mathbb R^4$. These
representations have been exhaustively studied in earlier papers. The group
$\g$ is identified with the kinematical symmetry group of noncommutative
quantum mechanics of a system with two degrees of freedom. The Wigner functions
studied here reflect different levels of non-commutativity -- both the
operators of position and those of momentum not commuting, the position
operators not commuting and finally, the case of standard quantum mechanics,
obeying the canonical commutation relations only.
