The main theme of the book is to study and analyse Restricted Three Body Problem after considering the perturbations such as Coriolis & Centrifugal forces, Potential function, Photogravitational and irregularities in the shapes of the primaries. The stability theory is divided in to two parts such as Linear stability and Non linear stability. In Non linear stability , we use KAM Theory. The book gives a precise information about restricted three body problem starting from Lagrange, Arnold, Zhebehly etc. till date.