  Field theoretical models with first order Lagrangean can be formulated in a
covariant Hamiltonian formalism. In this article, the geometrical construction
of the Gerstenhaber structure that encodes the equations of motion is explained
for arbitrary fibre bundles. Special emphasis has been put on naturality of the
constructions. Further, the treatment of symmetries is explained. Finally, the
canonical field theoretical 2-form is obtained by pull back and integration of
the polysymplectic form over space like hypersurfaces.
