Fano’s research trajectory on birational contact transformations of the plane

This paper investigates Gino Fano’s contributions to a special class of geometric transformations, the so-called “birational contact transformations of the plane”. His research in this field spanned over twenty years, from 1928 to 1947, a period marked by the progressive decline of the Italian School of algebraic geometry. In addition to publishing five articles on this topic, in 1944 Fano also delivered a lecture on these transformations at the Cercle Mathématique of Lausanne. The contents of this lecture are reconstructed from unpublished documents, whose critical edition is provided in the appendix.