  We define the {\it rest-frame instant form} of tetrad gravity restricted to
Christodoulou-Klainermann spacetimes. After a study of the Hamiltonian group of
gauge transformations generated by the 14 first class constraints of the
theory, we define and solve the multitemporal equations associated with the
rotation and space diffeomorphism constraints, finding how the cotriads and
their momenta depend on the corresponding gauge variables. This allows to find
quasi-Shanmugadhasan canonical transformation to the class of 3-orthogonal
gauges and to find the Dirac observables for superspace in these gauges.
  The construction of the explicit form of the transformation and of the
solution of the rotation and supermomentum constraints is reduced to solve a
system of elliptic linear and quasi-linear partial differential equations. We
then show that the superhamiltonian constraint becomes the Lichnerowicz
equation for the conformal factor of the 3-metric and that the last gauge
variable is the momentum conjugated to the conformal factor. The gauge
transformations generated by the superhamiltonian constraint perform the
transitions among the allowed foliations of spacetime, so that the theory is
independent from its 3+1 splittings. In the special 3-orthogonal gauge defined
by the vanishing of the conformal factor momentum we determine the final Dirac
observables for the gravitational field even if we are not able to solve the
Lichnerowicz equation. The final Hamiltonian is the weak ADM energy restricted
to this completely fixed gauge.
