群能够描述自然界的对称性，从而成为现代科学中最核心的数学概念和工具之一。研究群的基本工具是群的表示论，它是通过考察群作用的效果来了解这个代数结构本身。本文系统地阐述了有限群表示论的基本概念，并将有限群的表示问题转化为若干不可约表示的问题。由于任意群都同构于Sn的一个子群，所以我们重点讨论Sn的不可约表示问题。此外，本文还通过研究群的特征标理论来刻画群的结构，给出了计算特征标表具体步骤。并且将群表示问题扩张到群代数上去考虑，最终用杨图来实现n阶对称群的表示。

Groups can describe the symmetry of nature, thus they become the core of modern science in the mathematical concepts and tools . The basic tool to research groups is the theory of representation of groups.And the finite group's indivisible representation is one of finite group theory of representation basic issues. This paper elaborated the basic concepts of the finite group theory of representation systematically.Then we transform the questions concerning finite group's representation to indivisible representation ones, this paper portrays through researching character theory to learn the structure of group , and it has given concrete step of the computation character table .At the same time ,we expand the representation of group to the group algebra . Finally, we use Young diagram to discribe the representation of the symmetry group.