"The book is the first of three independent books whose aim is to describe methods of the analytic theory of differential equations such as monodromy, analytic continuation, resurgence, summability etc. It is aimed at graduate students, mathematicians and theoretical physicists." (Vladimir P. Kostov, zbMATH 1355.34003, 2017)

• Preface.-Preface to the three volumes.- Part I:Monodromy in Linear Differential Equations.- 1 analytic continuation and monodromy.- Differential Galois Theory.- Inverse Problems.- The Riemann-Hilbert problem.- Part II: Introduction to 1-Summability and Resurgence.- 5 Borel-Laplace Summation.- Resurgent Functions and Alien Calculus.- the Resurgent Viewpoint on Holomorphic Tangent-to-Identity Germs.- Acknowledgements.- Index.

"The book is the first of three independent books whose aim is to describe methods of the analytic theory of differential equations such as monodromy, analytic continuation, resurgence, summability etc. It is aimed at graduate students, mathematicians and theoretical physicists." (Vladimir P. Kostov, zbMATH 1355.34003, 2017)

• Preface.-Preface to the three volumes.- Part I:Monodromy in Linear Differential Equations.- 1 analytic continuation and monodromy.- Differential Galois Theory.- Inverse Problems.- The Riemann-Hilbert problem.- Part II: Introduction to 1-Summability and Resurgence.- 5 Borel-Laplace Summation.- Resurgent Functions and Alien Calculus.- the Resurgent Viewpoint on Holomorphic Tangent-to-Identity Germs.- Acknowledgements.- Index.