In the first decade of the 19th century, Jean Baptiste Joseph Fourier invented a technique using sums of trigonometric functions--called ``Fourier Series''--to solve the differential equations of heat conduction. Today, physicists, astronomers, engineers, and many others use Fourier series to analyze functions of time and space, solve differential equations, and compress data, to name just a few applications. We shall illustrate the simplest form of Fourier series using IDL (Interactive Data language).