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The theory of fixed points has been emerged as one of the most powerful and major theoretical tools of modern mathematics. In addition, by the development of accurate and efficient techniques for computing fixed points the effectiveness of the concept for applications have been increased enormously. In recent years fixed point theory has grown rapidly into a flourishing and dynamic field of study both in pure and applied mathematics. It has become one of the most essential tools in the study of nonlinear phenomena. The iterative methods for approximating fixed points are of great importance for modern numerical mathematics. In this work fixed point theorems for various classes of 1-set contraction mappings have been proved under different conditions. In the second part of the book several iteration processes have been constructed and convergence theorems are established for the class of Zamfirescu operators. This book and the recent references in it will be of great help for the young researchers in fixed point theory and those interested in this field of study.