Financial mathematics is one of the fastest developing areas generally used in modern banking and corporate finance, which, together with the evolution of modern financial products following the discovery of the Black-Scholes formula, provides rapid growth of new mathematical models. Furthermore, it has increased the demand by financial institutions for well-qualified mathematicians. The Black-Scholes model provides modern financial mathematics with the principle assumptions and the crucial concepts needed to understand the construction of models and evaluation of an optional value under the fluctuation of an asset price.This article aims to present the Black-Scholes model as the second order partial differential equation with boundary conditions and initial values for pricing European put and call options. It also shows examples of financial products in Thailand analyzed using this model, which reveals the same trend as the model predicts. The fundamental knowledge of the Black-Scholes model will lead to understanding other financial derivative models.