This volume contains contributions to the Séminaire de Mathématiques Supérieures NATO Advanced Study Institute on 'Morse theoretic Methods in non-linear Analysis and Symplectic Topology' which was held at the Université de Montréal in the summer of 2004. The recent years have witnessed the emergence of a deeper and more general formalism of the main geometric ideas in these fields. The surveys and research papers in this volume are a striking example of this trend. They provide an up-to-date overview of some of the most significant advances in these topics. The text is of high relevance for graduate students as well as for more senior mathematicians with interest in a wide range of topics going from symplectic topology to dynamical systems and from algebraic and differential topology to variational methods.