Contents

pp v-vi

Introduction

pp vii-x

Abstracts

pp 1-10

Part I - Dessins d'enfants

pp 11-12

Unicellular cartography and Galois orbits of plane trees

pp 13-24

Galois groups, monodromy groups and cartographic groups

pp 25-66

Permutation techniques for coset representations of modular subgroups

pp 67-78

Dessins d'enfants en genre 1

pp 79-116

Part II - Inverse Galois problem

pp 117-118

The regular inverse Galois problem over large fields

pp 119-138

The symplectic braid group and Galois realizations

pp 139-150

Applying modular towers to the inverse Galois problem

pp 151-176

Part III - Galois actions, braids and mapping class groups

pp 177-178

Galois group Gℚ, singularity E7, and moduli M3

pp 179-218

Monodromy of iterated integrals and non–abelian unipotent periods

pp 219-290

Part IV - Universal Teichmüller theory

pp 291-292

The universal Ptolemy group and its completions

pp 293-312

Sur l'isomorphisme du groupe de Richard Thompson avec le groupe de Ptolémée

pp 313-324

The universal Ptolemy-Teichmuller groupoid

pp 325-348

Errata for Tame and stratified objects

pp 349-349