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In General Relativity the total energy of an isolated gravitating system is described by a geometric invariant of asymptotically flat Riemannian 3--manifolds. One--parameter families of hypersurfaces foliating such a manifold can be used to encode and study global geometrical and physical properties such as the center of mass and energy inequalities. The article summarizes three lectures given at the conference on "Trends in Mathematical Physics" in Knoxville 1998
