Finite dimesional Hamiltonian formalism for gauge and field theories

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.Comment: 52 pages. In this paper we give a more general hamiltonian formulation for a gauge and field theories, it's an extension of our previous paper math-ph/000402