Abstract Fourier series is a way of representing periodic functions as a sum of sine and cosine terms, as the series consists of the sine and cosine terms, it often have an important physical interpretation of the nature of the phenomena. Fourier series has great importance in physics and engineering fields because most of the phenomena are periodic. This paper presents a systematic and comprehensive overview of the Fourier series along its applications in solving ordinary differential equations subject to periodic forcing function, partial differential equations subject to some auxiliary conditions and approximation of periodic functions.