This book is issued from a conference around resurgent functions in Physics and multiple zetavalues, which was held at the Centro di Ricerca Matematica Ennio de Giorgi in Pisa, on May 18-22, 2015. This meeting originally stemmed from the impressive upsurge of interest for Jean Ecalle's alien calculus in Physics, in the last years a trend that has considerably developed since then. The volume contains both original research papers and surveys, by leading experts in the field, reflecting the themes that were tackled at this event:  Stokes phenomenon and resurgence, in various mathematical and physical contexts but also related constructions in algebraic combinatorics and results concerning numbers, specifically multiple zetavalues.

Asymptotics, ambiguities and resurgence.- Nonlinear eigenvalue problems.- Feynman diagrams and their algebraic lattices.- Invariants of identity-tangent diffeomorphisms expanded as series of multitangents and multizetas.- The resurgent approach to topological string theory.- WKB and resurgence in the Mathieu equation.- Renormalised conical zeta values.- Combinatorics of Poincaré's and Schröder's equations.