The Hamiltonian formulation of classical field theory

In this paper I shall present some result from the theory of classical non-relativistic field theory and discuss how they might be useful in the general relativistic context. Some of the Hamiltonian formalism has already been successfully employed in the general relativistic context, but much more remains to be done in the area of dynamic stability, linearization stability, bifurcation, symmetry breaking, and covariant reduction.