Function approximations, interpolation, numerical differentiation and numerical integrations are very important topics in the numerical analysis. These topics are widely used and found in science and engineering applications. In the present chapter, we will present the main methods and techniques that had been developed for such topics. Differentiation and integration related together by so many relations as we will see later on. Finally, one can say that these topics are very important in our daily life, and therefore everyone should be aware of them.