  We present a covariant multisymplectic formulation for the Einstein-Palatini
(or Metric-Affine) model of General Relativity (without energy-matter sources).
As it is described by a first-order affine Lagrangian (in the derivatives of
the fields), it is singular and, hence, this is a gauge field theory with
constraints. These constraints are obtained after applying a constraint
algorithm to the field equations, both in the Lagrangian and the Hamiltonian
formalisms. In order to do this, the covariant field equations must be written
in a suitable geometrical way, using integrable distributions which are
represented by multivector fields of a certain type. We obtain and explain the
geometrical and physical meaning of the Lagrangian constraints and we construct
the multimomentum (covariant) Hamiltonian formalism. The gauge symmetries of
the model are discussed in both formalisms and, from them, the equivalence with
the Einstein-Hilbert model is established.
