In this talk, an introduction of classical Extreme Value Theory (EVT) is presented as a tool to understand the properties of the tail of the probability distribution of a stochastic variable. First, we take a look at the statistical behavior of \(M_n=\max \{X_1, X_2, \cdots, X_n\}\) where \(X_1, X_2, \cdots, X_n\) is a sequence of i.i.d. RV's having common distribution function \(F\). The result of classical EVT for independent processes was extended to apply to a wide class of dependent (stationary) sequences satisfying the \(D(u_n)\) and \(D'(u_n)\) conditions. Finally, I will mention one of the examples for EVT on a dynamical system such as the Arnold Cat Map.