The idea of this book germinated during the Luminy conference on “Geometry and Arithmetic of Moduli Spaces”, which took place in late August 1995. Our goal in organizing that conference was to encourage the natural generation of ideas which occurs when specialists in a domain are confined weeklong at close quarters with non-specialists who urgently need to learn about that domain for the purposes of their particular research. Moduli spaces are of course ubiquitous, but the research we particularly had in mind was any concerning topics in the early part of Grothendieck's Esquisse d'un Programme.

The Esquisse was not published earlier because Alexandre Grothendieck could not be found, much less his permission requested. It was during the Luminy conference that we learned from Jean Malgoire that he had obtained permission from Grothendieck to publish all and any of Grothendieck's mathematical manuscripts which lay in his possession; he told us of this and suggested that we include the Esquisse in a book of proceedings of the conference, a suggestion which we welcomed with enthusiasm. We thought of producing a book of proceedings which could appear as a kind of sequel to The Grothendieck Theory of Dessins d'Enfants, itself a volume of proceedings of a previous Luminy conference.

The inclusion of the Esquisse among the “contributions” generated enthusiasm among the participants certainly most unusual in such situations, and we quickly gathered more contributions than could be included in a single volume.