  {\sl A Hamiltonian framework for 2+1 dimensional gravity coupled with matter
(satisfying positive energy conditions) is considered in the asymptotically
flat context. It is shown that the total energy of the system is non-negative,
vanishing if and only if space-time is (globally) Minkowskian. Furthermore,
contrary to one's experience with usual field theories, the Hamiltonian is}
{\rm bounded from above}. This is a genuinely non-perturbative result. {\sl In
the presence of a space-like Killing field, 3+1 dimensional vacuum general
relativity is equivalent to 2+1 dimensional general relativity coupled to
certain matter fields. Therefore, our expression provides, in particular, a
formula for energy per-unit length (along the symmetry direction) of
gravitational waves with a space-like symmetry in 3+1 dimensions. A special
case is that of cylindrical waves which have two hypersurface orthogonal,
space-like Killing fields. In this case, our expression is related to the
``c-energy'' in a non-polynomial fashion. While in the weak field limit, the
two agree, in the strong field regime they differ significantly. By
construction, our expression yields the generator of the time-translation in
the full theory, and therefore represents the physical energy in the
gravitational field.} \footnote{$^1$}{This is a detailed account of the results
presented in the Brill-Misner symposium at the University of Maryland in
May1993}
