A completion is any of several related functors on rings and modules that result in complete topological rings and modules. It is among the most basic tools in analyzing commutative rings. The completion of a ring is useful in commutative algebra because it sometimes allows us to bring methods of analysis to bear on problems in algebra. One of the main aim of this talk is to explain smooth morphisms of rings which are one of the main ingredients in Desingularization. Moreover, we will also discuss number of morphism and regular morphisms of Noetherian rings and some of their interesting properties.