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The main focus is on the Hamilton-Jacobi techniques in classical generalrelativity that were pursued by Peter Bergmann and Arthur Komar in the 1960'sand 1970's. They placed special emphasis on the ability to construct the factorgroup of canonical transformations, where the four-dimensional diffeomorphismphase space transformations were factored out. Equivalence classes wereidentified by a set of phase space functions that were invariant under theaction of the four-dimensional diffeomorphism group. This is contrasted andcompared with approaches of Paul Weiss, Julian Schwinger, Richard Arnowitt,Stanley Deser, Charles Misner, Karel Kuchar - and especially thegeometrodynamical program of John Wheeler and Bryce DeWitt where diffeomorphismsymmetry is replaced by a notion of multifingered time. The origins of all ofthese approaches are traced to Elie Cartan's invariant integral formulation ofclassical dynamics. A related correspondence concerning the thin sandwichdispute is also documented.

Observables and Hamilton-Jacobi approaches to general relativity. I. The Earlier History