Abstract: We start with famous and well known classical models (Fermi-Pasta-Ulam model and Kicked Rotor) in order to discuss the concept of classical chaos, and methods of its determination. Specifically, we focus on the notions of ergodicity and mixing, the Lyapunov exponents and other definitions of chaos. We also discuss the less known mechanism of classical chaos which occurs in integrable systems, in view of next discussion of the definition of quantum chaos.