Einstein’s theory of general relativity provided an impetus to the development of differential geometry especially through the works of T. Levi-Civita, J. A. Schouten, D. Struik, O. Veblen, L. P. Eisenhart, and T. Y. Thomas. Also among these early developers were Weyl and Cartan, and this paper describes their common interest in transferring F. Klein’s transformation groups into a differential geometry setting and, in particular, generalizing the latter through use of infinitesimal group structures. Beginning with a 1918 paper and continuing in his book [Raum, Zeit, Materie. Vorlesungen über allgemeine Relativitätstheorie. Berlin: J. Springer (1918; JFM 46.1277.01)] and later, H. Weyl developed the first unified field theory. In the course of doing this, he maintained an interest in developing a purely infinitesimal geometry. This aspect of his work overlapped with Cartan’s interest but, in the latter’s case, led to a more general link between Kleinian geometry and Riemann’s differential geometry. The two read each other’s works and Weyl brought Cartan’s work to the attention of Princeton mathematicians in his 1929 visit there. The paper presents an interesting comparison of their complementary mathematical approaches.