●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......
內容簡介
辛幾何是近幾十年發展起來的新的重要數學分支。本書是辛幾何（新流形）的入門性讀物。。全書分為六章，分別是代數基礎、新流形、餘切叢、辛G-空間、Poisson流形、一個分級情形。前三章是重要的基本概念，後三章論述有關的應用。
