  In this paper the Dirac and Faddeev-Jackiw formulation for Einstein's theory
in the $G \rightarrow 0$ limit is performed; the fundamental Dirac's and
Faddeev-Jackiw brackets for the theory are obtained. First, the Dirac brackets
are constructed by eliminating the second class constraints remaining the first
class ones, then we fix the gauge and we convert the first class constraints
into second class constraints and the new fundamental Dirac's brackets are
computed. Alternatively, we reproduce all relevant Dirac's results by means of
the symplectic method. We identify the Faddeev-Jackiw constraints and we prove
that the Dirac and the Faddeev-Jackiw brackets coincide to each other. .
