  The first part of the series formulates the Einstein-Cartan theory in the
covariant hamiltonian framework. The first section revises the general
multisymplectic approach and introduces the notion of the d-jet bundles. Since
the whole Standard Model Lagrangian (including gravity) can be written as the
functional of the forms, the structure of the d-jet bundles is more appropriate
for the covariant hamiltonian analysis than the standard jet bundle approach.
The definition of the local covariant Poisson bracket on the space of covariant
observables is recalled. The main goal of the work is to show that the gauge
group of the Einstein-Cartan theory is given by the semidirect product of the
local Lorentz group and the group of spacetime diffeomorphisms. Vanishing of
the integral generators of the gauge group is equivalent to equations of motion
of the Einstein-Cartan theory and the local constraints algebra is closed Lie
algebra.
