We study the hypothesis where the universeU is a five-dimensional Riemannian manifold, wich satisfies certain global topological conditions. We postulate the existence of a principle of relativity wich treats on equal basis the live dimensions ofU; the laws wich satisfy this principle have an approximate description in a 4-dimensional space-time manifoldu; this gives the possibility of comparing them with the usual description of experimental laws. Thus, if we extend to the fifth dimension the invariance of general relativity, we obtainclassical electrodynamics: the equations of Maxwell, conservation of electricity, electromagnetic forces, etc. Likewise, the five-dimensional extension of the invariance of the wave equations leads one automatically to electromagnetic terms, such as they are actually observed; the electric charge, for instance, is found to be an integral multiple of anelementary charge which depends neither on the mass, nor on the spin. Among the other consequences of the theory, we findgauge invariance, andcharge conjugation; themaximum violation of parity in Β-decays; the existence oftwo neutrinos of opposite chirality.