  In a first part we propose an introduction to multisymplectic formalisms,
which are generalisations of Hamilton's formulation of Mechanics to the
calculus of variations with several variables: we give some physical
motivations, related to the quantum field theory, and expound the simplest
example, based on a theory due to T. de Donder and H. Weyl. In a second part we
explain quickly a work in collaboration with J. Kouneiher (math-ph/0211046) on
generalizations of the de Donder--Weyl theory (known as Lepage theories).
Lastly we show that in this framework a perturbative classical field theory
(analog of the perturbative quantum field theory) can be constructed.
