The scientific path of Jean Petitot develops between these two poles, topology and meaning. At stake it was to challenge the hiatus separating the exact sciences from the humanities that was the main point of the Petitot seminar of EHESS Epistemology of Models. By designing the appropriate qualitative dynamics between the two poles, form and meaning, it is possible to understand the Saussurian sign in structural semiotics, or the Greimasian semiotic square fordeep narrative structures or even the canonical formula of the myth of Lévi Strauss in structural anthropology. These are just few results in applying the theory of catastrophes to the emergence of meaning. The book is a collection of testimonies by distinguished authors who worked extensively with Jean Petitot in the different fields of Mathematics, Neurogeometry, Semiotics, Aesthetics, and Epistemology. An extensive bibliography of Petitot’s work is also presented.