The Maple command set is rich enough for generating Fourier series and graphing their partial sums. Yet, users have made these calculations more accessible by writing similar, but not identical packages for simplifying the pedagogical issues related to teaching Fourier series in the classroom. This month's article details how the built-in commands in Maple can implement the Fourier series and its related graphs. In coming articles, each of four different user-contributed Fourier series packages will be detailed.