This thesis based on the following paper [8]. In the qualitative theory of real planar polynomial differential systems two of the main prob-lems are the determination of limit cycles and the center-focus problem, i.e. to distinguish when a singular point is either a focus or a center. The notion of center goes back to Poincaré. He defined a center for a vector field on the real plane as a singular point having a neighborhood filled of periodic orbits with the exception of the singular point. the thesis organized as following, In chapter one we provide an introduction and slate the main results, In chapter two we provide basic difintions and theorems necessary to prov our main results. In chapter three the formal norms of our systems has been classified. In chapter 4 we prove our main theorem by providiny all different global phase portraits of our systems and finally we give the details of comoutation of the Grobner basis by Mathimatica in chapter 5.