We present an introduction to Berkovich s theory of non-archimedean analytic spaces that
emphasizes its applications in various fields. The first part contains surveys of a
foundational nature including an introduction to Berkovich analytic spaces by M. Temkin and
to étale cohomology by A. Ducros as well as a short note by C. Favre on the topology of some
Berkovich spaces. The second part focuses on applications to geometry. A second text by A.
Ducros contains a new proof of the fact that the higher direct images of a coherent sheaf under
a proper map are coherent and B. Rémy A. Thuillier and A. Werner provide an overview of their
work on the compactification of Bruhat-Tits buildings using Berkovich analytic geometry. The
third and final part explores the relationship between non-archimedean geometry and dynamics. A
contribution by M. Jonsson contains a thorough discussion of non-archimedean dynamical systems
in dimension 1 and 2. Finally a survey by J.-P. Otal gives an account of Morgan-Shalen's theory
of compactification of character varieties. This book will provide the reader with enough
material on the basic concepts and constructions related to Berkovich spaces to move on to more
advanced research articles on the subject. We also hope that the applications presented here
will inspire the reader to discover new settings where these beautiful and intricate objects
might arise.
