Steven Lehar ( email@example.com )
Fourier theory is pretty complicated mathematically. But there are some beautifully simple holistic concepts behind Fourier theory which are relatively easy to explain intuitively. There are other sites on the web that can give you the mathematical formulation of the Fourier transform. I will present only the basic intuitive insights here, as applied to spatial imagery.
Basic Principles: How space is represented by frequency
Higher Harmonics: "Ringing" effects
An Analog Analogy: The Optical Fourier Transform
Fourier Filtering: Image Processing using Fourier Transforms