Abstract: Most of the central problems of mathematics are developed around solving equations. Modern algebra, as one of the core courses of mathematics teacher education, is developed from the problem of finding the root-finding formula of algebraic equations. First of all, from the gradual development of the radical solution of algebraic equations, understand the development history and research ideas of modern algebra are understood. Furthermore, it explores the teaching reform of modern algebra from four aspects: the main line of the course process, the combination of course teaching content and specific examples, the inheritance of mathematical thinking methods in the course and the practical application of the course.

Key words: Modern algebra, Group, Ring, Field