《基础代数》是计算机系密码学与信息安全方向的一门数学基础知识课程。课程系统地介绍近世代数的群论，环论、域论和模论，使学生掌握群、环、域、模等的代数结构和性质。本课程是密码学的重要数学基础，通过本课程的学习，学生能够更好地理解和掌握现代密码算法和协议。同时，这是密码学中“椭圆曲线密码”分支的必备的数学基础。

The purpose of this curriculum is to give an elementary introduction to abstract algebra. The following parts are included:1. Preliminaries: An introduction to the basic ingredients of the algebraic system, such as sets and mappings of these sets.2. The theory of group: This is one of the most oldest and richest branches of abstract algebra. Group of transformations play an important role in geometry, and finite groups are fundamental in Galois’ discoveries in the theory of equations. These two fields provide the original impetus to the development of the theory of groups. In this part, we will study some basic and important concepts such as semi-group, group, isomorphism, homomorphism, subgroup, invariant subgroup, factor group, and transformation group.3. The theory of ring: Unlike the theory of groups which had essentially one source, namely, the study of sets of 1-1 transformations relative to resultant composition, the theory of rings has been fused out of a number of special theories. For this reason, it will appear to be somewhat less unified than the theory of groups. In this part, we mainly focus on some concepts such as integral domain, division ring, field, ideal, difference ring, isomorphism, homomorphism and anti-isomorphism. Also we will introduce some important special instances of rings such as matrix rings and quaternions. Finally we prove the analogue for rings of Cayley’s theory on goups. 3. The theory of field: the split fields and split degree. 4. The theory of modue: the extention of vector space over rings.