This text reflects the recent growth of interest in the study and application of symplectic geometry. It opens with an elementary section for students which describes the present state of symplectic geometry and topology. Subsequent chapters intended for the more advanced reader follow. It also includes recent developments and discusses the theory of topological classification of integrable Hamiltonian systems of differential equations with two degrees of freedom having nondegenerate integrals of motion.

Translated by: R. S. Wadhwa