The Fourier series is a powerful mathematical tool that allows us to represent periodic functions as an infinite sum of sines and cosines. The idea, introduced by Joseph Fourier in the early 19th century, is that even very complex repeating waveforms can be broken down into simpler trigonometric components. Each term in the series corresponds to a frequency component of the original function, with coefficients determining the amplitude of the sine and cosine waves. This makes the Fourier series