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

Finite dimensional Hamiltonian formalism for gauge and quantum field theories