Mathematics and theoretical computer science are closely connected by their interest in discrete phenomena, either the structural aspects that one can express through combinatorial properties, or algorithmic aspects, or finally, the numerous logical aspects. We concentrate on a specific part of this interaction, which is the study of the structural passage from the finite to the infinite structures. Traditionally, in combinatorics, this passage has been studied ever since the 1930s through the work of pioneers such as Paul Erdös, who compared the combinatorics of a single finite with a single infinite structure, for example through the Ramsey properties. In the last fifteen years or so, the emphasis has been on studying the infinite families of finite structures and the manner in which they are arranged to form an infinite one. This can be done either through the classical notion of the Fraïssé limit, through the Lovász’s notion of a graphon and connected notions of combinatorial limits studied by an ever-growing community of researchers, and finally, the set-theoretic limits such as the ones obtained by un ultraproduct or a morass. This type of question is what our school attempts to address. The school is the first, to our knowledge, to address this very timely topic from the point of view of both mathematics and theoretical computer science, with a half of the participants and speakers coming from each subject.