The majority of practical problems involving PDEs cannot be solved by analytic methods. Therefore it is expedient to study numerical methods, which lead to approximate solutions of PDEs. Today, with the advances in computer technology, increased speed and storage capacity, the implementation of computer programs for approximating the solutions of PDEs are becoming more and more accessible. In many introductory texts, the student is confronted with several approximation or iteration schemes, and then the student is simply asked to write computer programs to implement these schemes. While in some of the exercises we will also encourage the student to write computer programs, the primary goal of this chapter is to provide an understandable and precise introduction to the numerical solution of PDEs, as opposed to an encyclopedic cookbook of algorithms without explanations.