The general theory of relativity (GRT) introduces new difficulties, which concern both the generalization of space and time and the occurrence of gravitation. Einstein’s idea to relate gravitation as a special force to the metric and the affine connection of space-time via the equivalence principle raises a whole series of conceptual and epistemological questions. Since our problem will be mainly the reduction of the Newtonian theory of gravitation to the GRT, of those questions we only take up the problem of the conceptual integration of the Newtonian theory into GRT, and even only of the Poissonian version of it. This integration, which has to accomplish much more than the corresponding procedure in SRT, is perhaps the most beautiful example of how much can be done for a complete reduction of one theory to another already in the preliminary stage of mutual adaptation (by exact reductions). In spite of this achievement (due to E. Cartan), the complete reduction still did not succeed satisfactorily in the general case. The usual Newtonian approximation does not pass a rigorous test for its usefulness as a reduction. As a case study, we reconstruct the Kepler orbits as a (partial) individual limiting case of the Schwarzschild solution and give an outlook on the general case with reference to the notion of (general) limiting case reduction. - GRT has a rich correspondence structure, and there are reductions of special relativistic non-gravitational theories to GRT in addition to the Newtonian limiting case (and others). Here, we have to criticize the popular opinion that to every special relativistic theory, like classical electrodynamics, there exists something like the general relativistic generalization This cannot be the case, because due to Einstein’s equations in the presence of non-gravitational forces there must always be a genuine gravitational field, however weak it may be. Thus, we depend in all these cases on approximate reductions.