This chapter is concerned with the study of generalized equations. It uses the idea of restricted convergence domains to present a convergence analysis of generalized equation. The chapter finds larger convergence domain for the Newton’s method. By means of using the restricted convergence domains, it obtains a finer convergence analysis with tighter error estimates and precise information on the location of the solution. The chapter presents the local convergence study of the Newton's method and provides special cases and numerical examples.