  Symmetries and, in particular, Cartan (Noether) symmetries and conserved
quantities (conservation laws) are studied for the multisymplectic formulation
of first and second order Lagrangian classical field theories. Noether-type
theorems are stated in this geometric framework. The concept of gauge symmetry
and its geometrical meaning are also discussed in this formulation. The results
are applied to study Noether and gauge symmetries for the multisymplectic
description of the electromagnetic and the gravitational theory; in particular,
the Einstein--Hilbert and the Einstein--Palatini approaches.
