Providing an elementary introduction to analytic continuation and monodromy the first part of
this volume applies these notions to the local and global study of complex linear differential
equations their formal solutions at singular points their monodromy and their differential
Galois groups. The Riemann-Hilbert problem is discussed from Bolibrukh's point of view. The
second part expounds 1-summability and Ecalle's theory of resurgence under fairly general
conditions. It contains numerous examples and presents an analysis of the singularities in the
Borel plane via alien calculus which provides a full description of the Stokes phenomenon for
linear or non-linear differential or difference equations. The first of a series of three
entitled Divergent Series Summability and Resurgence this volume is aimed at graduate
students mathematicians and theoretical physicists interested in geometric algebraic or local
analytic properties of dynamical systems. It includes useful exercises with solutions. The
prerequisites are a working knowledge of elementary complex analysis and differential algebra.
