Symplectic and Contact Geometry A Concise Introduction

This textbook offers a concise introduction to symplectic and contact geometry, with a focus on the relationships between these subjects and other topics such as Lie theory and classical mechanics.

Organized into four chapters, this work serves as a stepping stone for readers to delve into the subject, providing a succinct and motivating foundation. The content covers definitions, symplectic linear algebra, symplectic and contact manifolds, Hamiltonian systems, and more. Prerequisite knowledge includes differential geometry, manifolds, algebraic topology, de Rham cohomology, and the basics of Lie groups. Quick reviews are included where necessary, and examples and constructions are provided to foster understanding.

Preface.- Symplectic linear algebra.- Symplectic manifolds.- Hamiltonian systems.- Contact manifolds.- References.- Index.

Anahita Eslami Rad is a Researcher at the mathematics department (FaMAF) of the National University of Cordoba, Argentina. She obtained her BSc and MSc in mathematics from the University of Tehran, Iran. Then she moved to Utrecht University, Netherlands, where she studied symplectic geometry and beyond. She received her PhD in mathematics from the Free University of Brussels, Belgium in 2012.