1 Some Algebra Basics
1.1 Skew-Symmetric Forms
1.2 0rthogonality Defined by a Skew-Symmetric 2-Form
1.3 Symplectic Vector Spaces, Symplectic Bases
1.4 The Canonical Linear Representation of s/(2, k) in the Algebra of the Skew-Symmetric Forms on a Symplectic Vector Space
1.5 Symplectic Groups
1.6 Symplectic Complex Structures
2 Symplectic Manifolds
2.1 Symplectic Structures on Manifolds
2.2 0perators of the Algebra of Differential Forms on a Symplectic
2.3 Symplectic Coordinates
2.4 Hamiltonian Vector Fields and Symplectic Vector Fields
2.5 Poisson Brackets Under Symplectic Coordinates
2.6 Submanifolds of Symplectic Manifolds
3 Cotangent Bundles
3.1 Liouville Forms and Canonical Symplectic Structures on Cotangent Bundles
3.2 Symplectic Vector Fields on a Cotangent Bundle
3.3 Lagrangian Submanifolds of a Cotangent Bundle
4 Symplectic G-Spaces
4.1 Definitions and Examples
4.2 Hamiltonian q-Spaces and Moment Maps
4.3 Equivariance of Moment Maps
5 Poisson Marufolds
5.1 The Structure of a Poisson Manifold
5.1.1 The Schouten-Nijenhuis Bracket
5.2 The Leaves of a Poisson Manifold
5.3 Poisson Structures on the Dual of a Lie Algebra
6 A Graded Case
6.1 (0, n)-Dimensional Supermanifolds
6.2 (0, n)-Dimensional Symplectic Supermanifolds
6.3 The Canonical Symplectic Structure on T*P
Bibliography
Index

辛几何是近几十年发展起来的新的重要数学分支。本书是辛几何（新流形）的入门性读物。。全书分为六章，分别是代数基础、新流形、余切丛、辛G-空间、Poisson流形、一个分级情形。前三章是重要的基本概念，后三章论述有关的应用。