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This work provides a general overview for the treatment of symmetries inclassical field theories and (pre)multisymplectic geometry. The geometriccharacteristics of the relation between how symmetries are interpreted intheoretical physics and in the geometric formulation of these theories areclarified. Finally, a general discussion is given on the structure ofsymmetries in the presence of constraints appearing in singular field theories.Symmetries of some typical theories in theoretical physics are analyzed throughthe construction of the relevant multimomentum maps which are the conservedquantities (by Noether's theorem) on the (pre)multisymplectic phase spaces.

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