Geometric Galois Actions: Around Grothendieck's Esquisse D'Un Programme

The first of two volumes on anabelian algebraic geometry, this book contains the famous manuscript "Esquisse d'un Programme" (Sketch of a Program) by Alexander Grothendieck. This work, written fourteen years after his retirement from public life in mathematics, includes the closely related letter to Gerd Faltings, published for the first time in this volume. Together these documents describe a powerful program of future mathematics, unifying aspects of geometry and arithmetic via the central point of moduli spaces of curves. The book is written in an artistic and informal style. It contains several articles on subjects directly related to the ideas explored in the manuscripts, including surveys of mathematics due to Grothendieck, explanations of points raised in the Esquisse, and surveys on progress in the domains described there.