This book presents numerical approximation techniques for solving various types of mathematical problems that cannot be solved analytically. In addition to well-known methods, it contains a collection of non-standard approximation techniques that appear in the literature but are not otherwise well known.  This text also contains original methods developed by the author.  It includes an extensive treatment of approximate solutions to various types of integral equations. Examples are used extensively to illustrate the theory.  Problems at the end of the chapters are provided for practice.   The book is suitable as a textbook or as a reference for students taking a course in numerical methods. Researchers in need of approximation methods in their work will also find this book useful.