  The jet formalism for Classical Field theories is extended to the setting of
Lie algebroids. We define the analog of the concept of jet of a section of a
bundle and we study some of the geometric structures of the jet manifold. When
a Lagrangian function is given, we find the equations of motion in terms of a
Cartan form canonically associated to the Lagrangian. The Hamiltonian formalism
is also extended to this setting and we find the relation between the solutions
of both formalism. When the first Lie algebroid is a tangent bundle we give a
variational description of the equations of motion. In addition to the standard
case, our formalism includes as particular examples the case of systems with
symmetry (covariant Euler-Poincare and Lagrange Poincare cases), variational
problems for holomorphic maps, Sigma models or Chern-Simons theories. One of
the advantages of our theory is that it is based in the existence of a
multisymplectic form on a Lie algebroid.
