Abstarct: Let C and P are Riemann shere and polynomial of degree d>=2 respectively. The Riemann shere can be divided into two totally invariant sets with respect to P: a stable set ,on which the dynamics of P is predictable, and an unstable set ,on which the dynamics of P is chaotic. In the language of complex analysis , the stable set for P is the set of point z in C for which the family of iterates of P is normal in some open neighborhood of z. the stable set of P is called the Fatou set. It haz several characterizations including the absence of normality as well as being the closure of repelling periodic orbits or the topological boundary of the unbounded Fatou component.