An Introduction to Fourier Theory: A mathematically inclined introduction with illustrations and explanations of related theorems, its properties and numerical methods for calculating transforms.
Fast Fourier Transform: Article in MathWorld.
Fast Fourier Transforms: Survey and history of FFT algorithms from Wikipedia.
Introduction To Fourier Transform: A description of the principle of fourier transform and subsequent derivation of formulae. Page includes graphs.
Introduction to the Fourier Transform: Notes on applications to Image Processing.
Mathematics of the Discrete Fourier Transform (DFT): Notes by Julius O. Smith III, Stanford.