In this chapter, we study an important and strange characteristic of a dynamical system known as chaos. It is the phenomenon observed in most of the natural processes where the happening of a particular thing depends very sensitively upon a number of parameters that change during the process. Before defining chaos, we will take a review of some of the basic concepts required like orbit of a fixed and periodic point of a mapping, the orbit diagram, etc. We also present a detailed classification of fixed and periodic points of a mapping in reference to their stability by means of some theorems.