Contents

Preface

Chapter 0. Some Aspects of Theoretical Mechanics

§0.1. The Lagrange equations

§0.2. Hamilton's equations

§0.3. The Hamilton-Jacobi equation

§0.4. A symplectic interpretation

§0.5. Hamilton's equations via the Poisson bracket

§0.6. Towards quantization

Chapter 1. Symplectic Algebra

§1.1. Symplectic vector spaces

§1.2. Symplectic morphisms and symplectic groups

§1.3. Subspaces of symplectic vector spaces

§1.4. Complex structures of real symplectic spaces

Chapter 2. Symplectic Manifolds

§2.1. Symplectic manifolds and their morphisms

§2.2. Darboux's theorem

§2.3. The cotangent bundle

§2.4. Kahler manifolds

§2.5. Coadjoint orbits

§2.6. Complex projective space

§2.7. Symplectic invariants (a quick view)