Abstarct: in this theses coefficient estimate for subclass of T and distortion for |f| , |f' | are investigated. Furthermore, subclasses of , as the class of starlike functions with negative coefficients, the class of convex functions with negative coefficients also the class of strongly starlike functions with negative coefficients and the class of strongly convex functions with negative coefficients are studied here.we investigate sufficient and necessary conditions on coefficient estimate for the class of strongly starlike functions.