  The aim of this paper is to generalize the classical Marsden-Weinstein
reduction procedure for symplectic manifolds to polysymplectic manifolds in
order to obtain quotient manifolds which in- herit the polysymplectic
structure. This generalization allows us to reduce polysymplectic Hamiltonian
systems with symmetries, such as those appearing in certain kinds of classical
field theories. As an application of this technique, an analogous to the
Kirillov-Kostant-Souriau theorem for polysymplectic manifolds is obtained and
some other mathematical examples are also analyzed. Our procedure corrects some
mistakes and inaccuracies in previous papers [29, 50] on this subject.
