The work on, and the understanding of, gravitation greatly influenced not only the physicist's conception of nature but also the development of all exact sciences. Newton invented the method of fluxions, and thereby laid down the foundations of calculus, in connection with his research on the motion of bodies and on the law of universal attraction.¹ The calculus of variations, the theory of differential equations and the perturbation methods of solving them arose directly from the needs of mechanics and astronomy. Through the work of Poincaré², the consideration of global and stable properties of motions stimulated the birth of topology. The relativistic theory of gravitation of Einstein³, and his search for a unified theory⁴, enhanced the development of differential geometry. The notion of a superspace introduced recently by J.A.Wheeler⁵ provides us with a concrete example of an infinite-dimensional manifold and leads to a number of difficult problems in the theory of Banach manifolds.