  We review the covariant canonical formalism initiated by D'Adda, Nelson and
Regge in 1985, and extend it to include a definition of form-Poisson brackets
(FPB) for geometric theories coupled to $p$-forms, gauging free differential
algebras. The form-Legendre transformation and the form-Hamilton equations are
derived from a $d$-form Lagrangian with $p$-form dynamical fields $\phi$.
Momenta are defined as derivatives of the Lagrangian with respect to the
"velocities" $d\phi$ and no preferred time direction is used. Action invariance
under infinitesimal form-canonical transformations can be studied in this
framework, and a generalized Noether theorem is derived, both for global and
local symmetries. We apply the formalism to vielbein gravity in $d=3$ and
$d=4$. In the $d=3$ theory we can define form-Dirac brackets, and use an
algorithmic procedure to construct the canonical generators for local Lorentz
rotations and diffeomorphisms. In $d=4$ the canonical analysis is carried out
using FPB, since the definition of form-Dirac brackets is problematic. Lorentz
generators are constructed, while diffeomorphisms are generated by the Lie
derivative. A "doubly covariant" hamiltonian formalism is presented, allowing
to maintain manifest Lorentz covariance at every stage of the Legendre
transformation. The idea is to take curvatures as "velocities" in the
definition of momenta.
