The book is designed for researchers, students and practitioners interested in using fast and efficient iterative methods to approximate solutions of nonlinear equations. The following four major problems are addressed: problems 1 shows that the iterates are well defined; 2nd problem concerns the convergence of the sequences generated by a process and the question of whether the limit points are, in fact solutions of the equation; problem 3 concerns the economy of the entire operations; and last problem concerns with how to best choose a method, algorithm or software program to solve a specific type of problem and its description of when a given algorithm succeeds or fails.The book contains applications in several areas of applied sciences including mathematical programming and mathematical economics. There is also a huge number of exercises complementing the theory. This book contains the latest convergence results for the iterative methods: Iterative methods with the least computational cost; Iterative methods with the weakest convergence conditions; and Open problems on iterative methods.