The theory of groups and Lie algebras is interesting for many reasons. In the mathematical viewpoint， it employs at the same time algebra， analysis and geometry. On the other hand， it intervenes in other areas of science， in particular in different branches of physic8 and chemistry. It is an active domain of current research.
　　The general theory of algebraic groups is studied in chapter8 21 to 28. The relations between Lie algebras and algebraic groups， which are fundamental to us， are established in chapters 23 and 24. Chapter 29 present8 applications of these relations to tackle the systematic study of Lie algebras. The reader will observe that the geometrical aspects have an important part in this study.In particular， the orbits of points under the action of an algebraic group plays a central role.