  We discuss in this paper the canonical structure of classical field theory in
finite dimensions within the {\it{pataplectic}} Hamiltonian formulation, where
we put forward the role of Legendre correspondance. We define the generalized
Poisson $\mathfrak{p}$-brackets which are the analogues of the Poisson bracket
on forms. We formulate the equations of motion of forms in terms of
$\mathfrak{p}$-brackets. As illustration of our formalism we present three
examples: the interacting scalar fields, conformal string theory and the
electromagnetic field.
