 In the period until 1930, the problem of paradoxes led naturally to and was subsumed under the investigation of logical calculi (its final by-product being the Hilbert-Ackermann textbook of 1928). This in turn opened the way to the simplification of type theory, to important generalizations of the notion of set, and to an almost final axiomatic elaboration of set theory (along the Zermelian route, but also following the new path opened up by Johann von Neumann). The basic logical tool is essentially axiomatic formal analysis.