  We construct a lagrangian geometric formulation for first-order field
theories using the canonical structures of first-order jet bundles, which are
taken as the phase spaces of the systems in consideration. First of all, we
construct all the geometric structures associated with a first-order jet bundle
and, using them, we develop the lagrangian formalism, defining the canonical
forms associated with a lagrangian density and the density of lagrangian
energy, obtaining the {\sl Euler-Lagrange equations} in two equivalent ways: as
the result of a variational problem and developing the {\sl jet field
formalism} (which is a formulation more similar to the case of mechanical
systems). A statement and proof of Noether's theorem is also given, using the
latter formalism. Finally, some classical examples are briefly studied.
