For the first time, the Sorbonne University Library is publishing the digitisation of part of the “Montessus de Ballore” archive kept at the Mathematics and Computer Science Research Library (Pierre and Marie Curie Campus). The publication on SorbonNum concerns the rich professional correspondence that Robert Montessus de Ballore (Villeurbanne 1870 - Arcachon 1937), a mathematician specialising in probabilities and algebraic continued fractions, received from more than two hundred correspondents, as well as eight drafts of letters that he had written for six different recipients. This collection also contains some notes and offprints relating to continued fractions. Senders of this scholarly correspondence include Paul Appell, Henri Bergson, Raymond Poincaré and Paul Valéry.