中文摘要：

在普吕克尔几何思想影响下,李开始研究切触变换,并将其从微分方程的一种工具提升为一个独立发展的理论.在李群理论创立过程中,李的切触变换研究及理论居于中心位置.其一,李的初衷是解微分方程,这促使他将几何学与微分方程联系起来,研究切触变换及其理论;其二,借助无穷小变换与切触变换的关系,李形成变换群的概念,并将其理论应用于解微分方程,将问题由对微分方程的分类导向对变换群的分类.李关于切触变换的研究不仅体现了李群起源的几何学特色,更体现了几何学在19世纪数学整体发展中所起到的作用.

英文摘要：

Under the impact of the idea of Plticker＇s geometry, contact transformations were up- graded from tools belonging differential equation into an independent theory due to Lie＇s research Lie＇s theory of contact transformations was in the centre of the process of establishment of Lie group theory. Firstly, Lie aimed to solve differential equations. This led him to study contact transforma- tions by mixing up geometry and differential equations. Secondly, basing on the relationship between infinitesimal and contact transformations, Lie created the concept of transformation groups. He further applied theory of transformation group to solve differential equations, and made the switch from clas-sification of differential equations to that of transformation groups. His research has showed the geoetrical feature in the genesis of Lie group, as well as the effect of geometry to the overall development of mathematics in the 19＇h century.