I needed some references which involves, the basic definition and motivation for Entanglement Entropy, and its one or two applications to many-body physics/black holes.
The standard reference for quantum information is Nielsen and Chuang, Quantum Computation and Quantum Information. Here is the Google books preview.
On the free side, I strongly recomment the "Quantum Entanglement" review by Horodecki brothers (they are quite famous in quantum information). It contains almost anything you'd want to know about entanglement and references to the rest. You can download it freely from arXiv: http://arxiv.org/abs/quant-ph/0702225
None of these require you to learn either many body theory or quantum field theory. But for many body theory and QFT, this is usually a good choice Quantum Field Theory of Many Body Systems. I'm afraid when it comes to quantum many body theory, basic QFT is a must and you will not be able to do without it.
I don't know the subject, but I found interesting resources below, I hope it will help you :