Professors R. de Ritis and G. Marmo took the initiative in the project and convinced us that a translation of this work of Cartan's
is long overdue. Their quiet efficiency also made the project a pleasure
to all participants. Professor H. Cartan went through the manuscript
with great care and made numerous suggestions for improvements.
His insight was particularly helpful in translating technical French terms
which do not have a canonical analog in English. Professor A. Trautman
kindly agreed to write a detailed Forward. His comments — especially
the exposition of Cartan's ideas in the language of modern differential
geometry — have greatly simplified our task. To all four, we are most
grateful.
This work was supported in part by the Alfred P. Sloan Foundation
and by the National Science Foundation of the United States.