This book is based on a conference concerning 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, in recent years, in Jean Ecalle's alien calculus in Physics. 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.