  This is a substantially expanded version of a chapter-contribution to "The
Springer Handbook of Spacetime", edited by Abhay Ashtekar and Vesselin Petkov,
published by Springer Verlag in 2014. This contribution introduces the reader
to the reformulation of Einstein's field equations of General Relativity as a
constrained evolutionary system of Hamiltonian type and discusses some of its
uses, together with some technical and conceptual aspects. Attempts were made
to keep the presentation self contained and accessible to first-year graduate
students. This implies a certain degree of explicitness and occasional reviews
of background material.
