The equivalent notions of Galois connexions, and of residual and residuated maps occur in a great varieties of \pure" as well as \applied" mathematical theories. They explicitly appeared in the framework of lattice theory and the rst of these talks is devoted to the history of their appearance and of the revealing of their links in this framework. So this talk covers more or less the period between 1940 (with the notion of polarity de ned in the rst edition of Birko 's book Lattice theory) and 1972 (with Blyth and Janowitz's book Residuation theory), a period containing fundamental works like Ore's 1944 paper Galois connexions or Croisot's 1956 paper Applications residuees.