In this chapter, we will discuss the elementary concepts associated with classical billiards. In a billiard system, a particle, or a non-interacting set of them, moves inside a closed region of space bounded by a border. The time evolution of the particles is described using a discrete mapping of the variables that define the particle’s position on the boundary, as well as the orientation of its trajectory after the collision. One variable may be the polar angle, and the other the angle between the particle’s trajectory and the tangent vector to the boundary at the instant of collision. We will consider three types of boundaries that lead to distinct dynamics. One is the circular billiard, whose boundary has a circular shape. Another is the elliptical billiard, and finally, we illustrate the dynamics with the ovoid billiard. The first two lead to integrable dynamics, whereas the last one exhibits a phase space containing chaos, stability islands, and invariant spanning curves, which are destroyed beyond a critical parameter, thus representing a non-integrable dynamics.