The first part of a two-volume set offering a systematic explanation of symplectic topology. This volume covers the basic materials of Hamiltonian dynamics and symplectic geometry.

Yong-Geun Oh is Director of the IBS Center for Geometry and Physics and is Professor in the Department of Mathematics at POSTECH (Pohang University of Science and Technology) in Korea. He was also Professor in the Department of Mathematics at the University of Wisconsin, Madison. He is a member of the KMS, the AMS, the Korean National Academy of Sciences, and the inaugural class of AMS Fellows. In 2012 he received the Kyung-Ahm Prize for Science in Korea.

Preface; Part I. Hamiltonian Dynamics and Symplectic Geometry: 1. Least action principle and the Hamiltonian mechanics; 2. Symplectic manifolds and Hamilton's equation; 3. Lagrangian submanifolds; 4. Symplectic fibrations; 5. Hofer's geometry of Ham(M, ¿); 6. C0-Symplectic topology and Hamiltonian dynamics; Part II. Rudiments of Pseudoholomorphic Curves: 7. Geometric calculations; 8. Local study of J-holomorphic curves; 9. Gromov compactification and stable maps; 10. Fredholm theory; 11. Applications to symplectic topology; References; Index.