This chapter shows applications of classical Fourier series. The following topics are treated in respective sections: the best approximation in quadratic mean (RMS approximation), periodic convolution and its role in AC Circuit calculations, the boundary value problem for the 2D-potential equation on a circular disk with the Poisson integral formula, the classical solution for the vibrating string, the approximation theorem of K. Weierstrass, and the 1/f theorem of N. Wiener. Examples and exercises are provided. These include, for example, the inhomogeneous vibrating string, the homogeneous one-dimensional heat equation, periodic convolution of given periodic functions, and Kepler’s equation.