This chapter offers both theoretical and practical perspectives on the Fourier series. It begins by drawing inspiration from periodic behaviors observed in nature, illustrating the motivation for using the Fourier series. The chapter then explores the Fourier series expansion of odd and even functions, which enables efficient decomposition of signals with particular symmetries and simplifies complex signal representations. Moving further, it introduces the complex number representation of the Fourier series, a powerful method for compactly expressing periodic functions. This approach is extended with the double Fourier series, facilitating the representation of functions that depend on two variables and are useful in multidimensional signal processing. Practical examples of Fourier series expansions for commonly encountered signals are provided, demonstrating the versatility and wide applications of Fourier analysis.