Many scientific and real-world problems that occur in science, engineering, and medicine can be represented in the form of differential equations and integral equations. There is a vital role of integral equations in studying different types of real-world problems to study the behavior of the issues. Thus, it becomes essential to know the various methods of finding solutions of the integral equation in explicit form. This textbook entitled Numerical approximation of Linear and Nonlinear Integral Equations is intended to study the methods of finding the explicit solutions of integral equations wherever possible and in the absence of finding an exact solution. It is intended to study the properties of solutions of the given integral equations. This book is based on syllabi of the theory of integral equations prescribed for the undergraduate and postgraduate students of mathematics in different institutions and universities worldwide. This book is also helpful for the competitive examinations as well.