There are several ways of describing a curve. One way is to use the equations and another way is to describe it via parametrization. The simple singularities of functions discovered, in so far as the property of being simple is concerned, by V. I. Arnol'd have been the object of much interest. Arnol'd classi ed simple germs by using defi ning equation of curve. In 1982. J. W. Bruce and T.J. Gafney study the simple singularities of parameterized plane curve over the fi eld of complex numbers. In this talk, I will try to explain some basic notions of local analytical geometry. Moreover, I will classify simple parameterized plane curve by using invariants.
