This project related to control systems, Lie groups and Lie algebra. Firstly, we have dis- cussed about control systems with its examples. Then various types of control systems and its applications. Control theory has continued to advance with advancing technology and has emerged in modern times as a highly developed discipline. Lie theory, the theory of Lie groups, Lie algebras and their applications is a fundamental part of mathematics. On this project review Lie groups controllability for left-invariant control systems on Lie groups are addressed