I'm looking to learn some theory about data/audio/video compression, and would be glad to get some recommendations. Online and print resources are both fine.
I'd like to recommend The Data Compression Book by Mark Nelson and JL Gailly 2nd Edition (M&T Books NY 1995).
This book is out of print, but as is the case with older editions, it is very easy to find it second hand or possibly digital copies.
The interest of the book, is that it covers all the fundamental compression algorithms. Given its age it is a bit outdated with regards to some of the recent audio and video compression tricks but one will be better prepared to study these after covering the older/fundamental algorithms. It is maybe a case where an older source is preferable.
A possible negative for this book is its use of the C language to implement the various algorithms. While C probably remains the language of choice for many compression libraries, current readers may be more comfortable with other languages.
It is otherwise, IMHO [and I'm glad to note, seconded or firsted, by Greg Hewgill] a very good book to get involved with data compression.
Edit: Sorry, I just noted this question is a duplicate of this SO question. Interestingly, "The Data Compression Book" wasn't mentioned in this other question.
I recommend The Data Compression Book by Mark Nelson. Unfortunately it appears to be out of print, but you should be able to find used copies.
I must say that I don't have much experience in this field, but I recently encountered a book that seemed very good, which also happens to be available for free online:
(Information Theory, Inference, and Learning Algorithms)
http://www.inference.phy.cam.ac.uk/mackay/itila/book.html
It might seem like it's about several different subjects, but the author's point seems to be that they're all actually the same, so you need to learn all of them to really get it.