A principal bundle E over a space X ( or a G-bundle, for short ) is a space E onwhich G operates (from the right ) and a G-invariant morphism p: E ~ X which is locally trivial in the etale topology, i.e. for every point x of X there is a neighbourhood U of x and an etale covering f: U' ~ U such that there is a G-equivariant isomorphism of f(E) with U'x G over U' where G operates by right translations on the second factor of U' x G.