  Given a foliation S of a manifold M, a distribution Z in M transveral to S
and a Poisson bivector \Pi on M we present a geometric method of reducing this
operator on the foliation S along the distribution Z. It encompasses the
classical ideas of Dirac (Dirac reduction) and more modern theory of J. Marsden
and T. Ratiu, but our method leads to formulas that allow for an explicit
calculation of the reduced Poisson bracket. Moreover, we analyse the reduction
of Hamiltonian systems corresponding to the bivector \Pi.
