Abstract algebra, also called modern algebra, came into being in19th century. Galois [181-1832] used the concept of "group" in1832, which completely solved the possibility of solving rooted algebraic equations. He was the first mathematician who put forward the concept of "group" and is generally called the founder of modern algebra. He changed algebra from the science of solving equations to the science of studying algebraic operation structure, that is, he pushed algebra from elementary algebra to abstract algebra.

Abstract algebra includes group theory, ring theory, Galois theory, lattice theory, linear algebra and many other branches. Combined with other branches of mathematics, new mathematical disciplines such as algebraic geometry, algebraic number theory, algebraic topology, topological groups, etc. Abstract algebra is also one of the foundations of modern computer theory.

Abstract algebra has an important influence on all modern mathematics and other scientific fields. Abstract algebra is developing with the development and application of various branch theories in mathematics. Following the work of boekhoff, von Neumann, kantorovich and Si Tong in 1933- 1938, lattice theory established its position in algebra. Since the mid-1940s, as a generalization of linear algebra, modular theory has been further developed and exerted a far-reaching influence. New fields such as universal algebra, homology algebra and category have also been established and developed.

Abstract algebra contains many branches, such as groups, rings, Galois theory, lattice theory, etc. It combines with other branches of mathematics to produce new mathematical disciplines, such as algebraic geometry, algebraic number theory, algebraic topology, topological groups, etc.

Mathematicians in China began to study abstract algebra in 1930s. Significant and important achievements have been made in many aspects, especially the work of Ceng Jiong Zhi, Hua and Zhou Weiliang.

The basic course of modern mathematics is being updated. In the 1950s, the teaching plan of the Department of Mathematics focused on "Advanced Calculus", "Advanced Algebra" and "Advanced Geometry". Today, people think that it is not enough to rely on this "old three highs" alone, and we should develop "new three highs", namely abstract algebra, topology and functional analysis. Modern mathematical theory is supported by these three pillars.