 In 1915 Einstein introduced general relativity, and our conception of the universe is based on it. General relativity rests on a conception of space and time—or better, space-time matter—that stands in opposition to the Newtonian one we have described above. In Einstein’s theory, space-time is deformable and its shape depends on the presence of matter. Space-time is, in technical terms, a four-dimensional manifold. We may think of an \(n\)-dimensional manifold as a set of \(n\)-tuples of real numbers. The spatial section of a four-dimensional manifold of space-time is a three-dimensional manifold (one can think of it as a set of triples of real numbers), and when cosmologists ask about the shape of the universe they try to characterize this three-dimensional manifold. The curvature of space-time corresponds to gravitation, and light rays and other material particles follow the geodesics (shortest paths) in the manifold. In general, the geodesics differ depending on the matter-energy content of the space being considered. The geodesics of the surface of the sphere (i.e. a two-dimensional surface) are portions of great circles. In the Euclidean plane, they are segments of straight lines. There are analogous notions for four-dimensional manifolds. Einstein’s equations for general relativity describe how the matter-energy content of the universe determines the geometry of space-time. The equations also yield cosmological models, which must be tested by empirical observation. The equations allow for multiple solutions and, as Alexander Friedmann (1924) observed, “in the absence of additional hypotheses, Einstein’s equations for the universe do not allow to definitely answer the question of the finiteness of the universe”. Let us briefly explain what is at stake in this comment, by pointing out the role of curvature and topology with respect to the issue of finiteness vs. infiniteness of our universe in relativistic cosmology. Topology is the branch of geometry that classifies spaces according to whether they can be transformed into one another “continuously”, that is with transformations that do not lead to cuts or tears.