References on the physics of anyons

One of the best recent references is the 2008 RMP article by Nayak et al. Non-Abelian Anyons and Topological Quantum Computation

A somewhat less technical reference is An Anyon Primer by Sumathi Rao.

There are many others but these two are good for someone starting out.

Ady Stern, Anyons and the quantum Hall effect - a pedagogical review, arXiv:0711.4697 is a gentle introduction.

In the presence of magnetic field, I like very much the contribution of S. Ouvry in the Séminaires Poincaré.