Sources to learn more about Audio/Video compression, codecs, algorithms etc. I was quite surprised when I learned the fact that the MP3 codec is extensively based on the Fourier Transform. I'd like to learn more about these topics in general. When I say more I mean the working principles of these technologies.

For even more clarity, I would prefer something like this video produced by Xiph.org
Compression codecs and methods are also based extensively in the field of Psychoacoustics.  For this, I thoroughly recommend the books available from the Focal Press, such as this one