Many problems of stability in the theory of dynamical systems face the difficulty of small divisors. The most famous example is probably given by Kolmogorov-Arnold-Moser theory in the context of Hamiltonian systems, with many applications to physics and astronomy. Other natural small divisor problems arise considering circle diffeomorphisms or quasiperiodic Schroedinger operators. In this volume Hakan Eliasson, Sergei Kuksin and Jean-Christophe Yoccoz illustrate the most recent developments of this theory both in finite and infinite dimension. A list of open problems (including some problems contributed by John Mather and Michel Herman) has been included. TOC:Hakan Eliasson: Perturbations of Linear Quasi-Periodic System.- Sergei B. Kuksin: KAM-Persistence of Finite-Gap Solutions.- Jean-Christophe Yoccoz: Analytic Linearization of Circle Diffeomorphisms.- Stefano Marmi and Jean-Christophe Yoccoz: Some Open Problems Related to Small Divisors.

Perturbations of linear quasi-periodic system.- KAM-persistence of finite-gap solutions.- Analytic linearization of circle diffeomorphisms.- Some open problems related to small divisors.