This thesis is devoted to the study of Complex analytic functions define on H = {w : w < 1}. The main objective of thesis is to obtain the relationship between new and existing classes of analytic functions using techniques of convolution and subordination. Let ST and CV represents the classes of starlike and convex functions respectively. We obtain many subclasses of uniformly convex and uniformly starlike functions by using different parameter. For these classes coefficient bounds, distortion and growth theorems are obtained. For these classes radii of close-to-convexity, convexity and starlikeness are derived . Further, we investigate that these classes are closed under generalized Bernardi integral operator. A natural generalization of Mocanu class is introduced. Many interesting and valuable results are obtained for this class.