After his work on connections and generalized spaces between 1922 and 1925, Élie Cartan began laying the foundation of the topological and geometric study of Lie groups and homogeneous spaces (1925–1930). We will endeavour to establish that the emergence of global questions is but part and parcel of a thorough restructuring around the epistemological polarity between local and global, a restructuring that occurs at three levels : a theoretical level, a thematic level and a rhetorical level. This new central polarity replaced a 19th century polarity between the infinitesimal and the finite. Our chronological exposition of Cartan's work in the period between 1922 and 1930 will pay special attention to modes of writing, comparing with the works of Hermann Weyl and Otto Schreier. We shall see, in particular, that in spite of the stability of terms such as “neighbourhood”, “manifold” or “group”, the meaning of these words underwent a dramatic change after 1925.