Over the last number of years powerful new methods in analysis and topology have led to the development of the modern global theory of symplectic topology, incl

The goal of these notes is to provide a fast introduction to symplectic geometry for graduate students with some knowledge of differential geometry, de Rham the

Symplectic geometry is a central topic of current research in mathematics. Indeed, symplectic methods are key ingredients in the study of dynamical systems, dif

This first edition of this book quickly became an established text in this fast-developing branch of mathematics. This second edition has been significantly rev

Symplectic geometry has its origins as a geometric language for classical mechanics. But it has recently exploded into an independent field interconnected with