Lie algebra is a mathematical concept introduced by Norwegian mathematician Sofus Lee when he studied continuous transformation groups in the late19th century, which is closely related to the study of Lie groups. Earlier, it appeared in mechanics in an implicit form, and its premise was the concept of "infinitesimal transformation", which can be traced back to the beginning of calculus at least. One of the earliest facts that can be expressed in Lie algebraic language is about the integration of Hamilton equation. Starting with discussing the structure of finite simple groups with r parameters, Lie discovered four main types of Lie algebras. In the paper 1894, French mathematician Jia Dang gave a complete classification of all simple lie algebras with variables and parameters in the complex field. Both he and the German mathematician Keeling found that all simple lie algebras are divided into four types and five exceptional algebras, which are also constructed by Adam. Katan and German mathematician William also used representation theory to study Lie algebra, and the latter got a key result. The term "Lie algebra" was introduced by john williams in 1934. With the passage of time, Lie algebra plays an increasingly important role in mathematics, classical mechanics and quantum mechanics. In 1980s, Lie algebra was no longer just understood as a tool for linearization of group theory, but as the source of many important problems in finite group theory and linear algebra. Lie algebra theory is constantly improving and developing, and its theories and methods have penetrated into many fields of mathematics and theoretical physics.