Donaldson-Auroux理论是关于如何在闭（紧无边）辛流形中构造闭辛子流形, 本文对这一理论做了一个引论性质的介绍. 我们补充了{D96}中的一些细节, 并对一些具体的构造过程做了改变, 我们认为这些工作会使得该理论容易被研究生所接受. 论文分为三章.在第一章中, 我们简单的介绍了这一理论的相关背景, 并对构造过程做了一个框架性的描述. 在第二章中, 我们仔细的介绍了相关的预备知识; 特别的，我们对Kahler角做了一个详细的讨论, 它给出了一个复向量空间的所有余二维子空间的一个有用的分类. 具体的构造过程可以分为两部分, 我们将其放在第三章中. 第一部分是构造紧辛流形上的复线丛的近全纯截面; 第二部分是对得到的近全纯截面做一个全局的扰动获得控制横截性. 而满足控制横截性的近全纯截面的零点集就给出了辛子流形.

In this master thesis, we give an introduction to the Donadson-Auroux theory, which is about the construction of symplectic submanifolds on a closed symplectic manifold. We complete many details to [D96] and make some changes in the illustration of concrete construction procedure. We think that these efforts can make this theory friendly enough to graduate students. This thesis is divided into three chapters.In chapter 1, we give a brief background of this theory, the strategy of the construction and the main result in D96. In chapter 2, we carefully introduce the prerequisite knowledge. Particularly, we have a very detailed discussion on the Kahler angle, which gives a useful classification of the subspaces with codimension $2$ of a complex vector space. We leave the main construction procedure which can be divided into two parts in chapter 3. The first part is the construction of asymptotically holomorphic sections on the complex line bundle over a compact symplectic manifold. And the second part is to use a global process of perturbation to obtain controlled transversality. The zero set of the asymptotically holomorphic section which satisfies the controlled transversality will give us the symplectic submanifold.