This book is a revised and enlarged second edition of the first edition published in 2002. It provides a comprehensive survey of the most significant contributions to the approximation of fixed points of nonlinear contractive type mappings. The book focuses on constructive fixed point theorems, which not only establish the existence and uniqueness of fixed points but also provide methods for approximating them and information on the data dependence or stability of the iterative methods. The second edition includes 111 exercises, applications, and miscellaneous results distributed across all chapters, enhancing the coverage of the topic. Seven new sections were added or expanded, and several sections were revised. Chapter 9 was significantly enlarged with recent results on the numerical comparison of fixed point iteration procedures. New numerical examples were added using the software package FIXPOINT. The bibliography was updated with over 500 new entries, resulting in more than 1575 references, reflecting the dynamic nature of the research field. The main merits of the second edition include a better presentation of the material and the systematic application of criteria for evaluating and presenting existing literature. The book also highlights new directions of research and less important topics for theoretical and numerical purposes. Chapter 9, along with sections 3.5, 5.5, 6.4, and 6.5, includes recent results that could influence future research in the area. The book aims to provide an in-depth and up-to-date coverage of the most significant 400 recent articles in the field. It includes a detailed bibliography with over 1575 references, focusing on innovative research. The author acknowledges the contributions of various colleagues and friends, as well as the support of his family. The book is intended as an introductory approach to iterative approximation of fixed points and welcomes comments and suggestions for future revisions.This book is a revised and enlarged second edition of the first edition published in 2002. It provides a comprehensive survey of the most significant contributions to the approximation of fixed points of nonlinear contractive type mappings. The book focuses on constructive fixed point theorems, which not only establish the existence and uniqueness of fixed points but also provide methods for approximating them and information on the data dependence or stability of the iterative methods. The second edition includes 111 exercises, applications, and miscellaneous results distributed across all chapters, enhancing the coverage of the topic. Seven new sections were added or expanded, and several sections were revised. Chapter 9 was significantly enlarged with recent results on the numerical comparison of fixed point iteration procedures. New numerical examples were added using the software package FIXPOINT. The bibliography was updated with over 500 new entries, resulting in more than 1575 references, reflecting the dynamic nature of the research field. The main merits of the second edition include a better presentation of the material and the systematic application of criteria for evaluating and presenting existing literature. The book also highlights new directions of research and less important topics for theoretical and numerical purposes. Chapter 9, along with sections 3.5, 5.5, 6.4, and 6.5, includes recent results that could influence future research in the area. The book aims to provide an in-depth and up-to-date coverage of the most significant 400 recent articles in the field. It includes a detailed bibliography with over 1575 references, focusing on innovative research. The author acknowledges the contributions of various colleagues and friends, as well as the support of his family. The book is intended as an introductory approach to iterative approximation of fixed points and welcomes comments and suggestions for future revisions.