The main theme of the book is to study linear and non-linear stability of the equilibrium points in the Robe's circular restricted three body problem using KAM theory. The book is divided into 5 chapters. Chapter 1 is introductory. In Chapter 2, the existence and linear stability of equilibrium points in the Robe's restricted three body problem is discussed when the 1st primary is an oblate spheroid. In Chapter 4 & 5 non linear stability of equilibrium point are studied using KAM theory. In these chapters, one can see the application of KAM theory in a very simplified manner. These chapters will give an important idea how the complex KAM theory works and is applied in the study of non linear stability and will help in understanding this complex theory.