The conference is intended to give an account of the new results concerning algebraic methods in dynamical systems. Morales-Ramis theorem establishing the quasi-abelianity of the differential Galois group of the variational equation along a particular solution of a meromorphically completely integrable Hamiltonian system have led during the recent years to a big number of new results on non-integrability of Hamiltonian systems. More recently, the application of differential Galois theory to the study of Hamiltonian systems is no longer limited to Picard-Vessiot theory but is extended to the more general setting based on recent results of Malgrange and Umemura.(source: www.esf.org)