Combinatorial Nullstellensatz is a powerful technique having many deep applications in a wide range of combinatorics problems. Its basic idea is to translate combinatorial questions into pure algebra, more precisely - into some properties of polynomials of several variables. The main founder of this method is Noga Alon, an outstanding contemporary mathematician from Israel. During the talk we will investigate the formulation of this technique presented by Alon in 1999 and we will show its elegant application to the celebrated Cauchy-Davenport theorem. Some list of problems and hints, for further individual studies, will also be presented.