One of fundamental results on local geometry of nondegenerate real hypersurfaces in complex space is the construction of normal forms developed by S. S. Chern and J. Moser. We will discuss a generalization of this construction to Levi degenerate hypersurfaces of finite type in $\Bbb C^2$. As a main consequence, using a convergence result of M. S. Baouendi, P. Ebenfelt and L. P. Rothschild, we obtain an explicit solution to the problem of local biholomorphic equivalence. Another application gives precise information on the dimension of the stability group. We will also mention some open problems for hypersurfaces in higher dimensions.