  We present a detailed examination of the variational principle for metric
general relativity as applied to a ``quasilocal'' spacetime region $\M$ (that
is, a region that is both spatially and temporally bounded). Our analysis
relies on the Hamiltonian formulation of general relativity, and thereby
assumes a foliation of $\M$ into spacelike hypersurfaces $\Sigma$. We allow for
near complete generality in the choice of foliation. Using a field--theoretic
generalization of Hamilton--Jacobi theory, we define the quasilocal
stress-energy-momentum of the gravitational field by varying the action with
respect to the metric on the boundary $\partial\M$. The gravitational
stress-energy-momentum is defined for a two--surface $B$ spanned by a spacelike
hypersurface in spacetime. We examine the behavior of the gravitational
stress-energy-momentum under boosts of the spanning hypersurface. The boost
relations are derived from the geometrical and invariance properties of the
gravitational action and Hamiltonian. Finally, we present several new examples
of quasilocal energy--momentum, including a novel discussion of quasilocal
energy--momentum in the large-sphere limit towards spatial infinity.
