Which books deal with DFT/FFT?
Basically, I've already read about this subject in the book "Introduction to Algorithms" (CLRS), but I think it lacks of the mathematical aspects of the DFT, presenting DFT as a transform from coefficient-form to point-form, rather than presenting it as change of basis transformation.
You could look at Foundations of Signal Processing by Vetterli et al, or Mathematical Methods and Algorithms for Signal Processing by Moon and Stirling.
Most introductory signal processing texts will have some coverage, though not necessarily in the matrix view. You can also use wikipedia.
As for FFT's, they're just an fast algorithm for computing DFT's; books like Discrete-Time Signal Processing by Oppenheim and Schafer have a chapter on this sort of thing (also Proakis' Digital Signal Processing, etc.).
One important part of the discrete fourier transform is that it diagonalizes circulant operators (i.e. circular convolution). And circular convolution is related to linear convolution, which is what a linear time invariant system does (convolves its impulse response with the input). Thus, the basis provided by the DFT is a special one (it's not an arbitrary orthonromal basis).