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.
Symplectic geometry in euclidean space;symplectic geometry on smooth manifolds; Hamiltonian systems with symmetries on symplectic manifolds; geodesic flows on two-dimensional Riemann surfaces; effective methods of constructing completely integrable systems on lie algebras; a brief review of the theory of topological classifications of integrable nondegenerate Hamiltonian equations with two degrees of freedom.