Quantum spin liquids
  These notes are an introduction to a few selected theoretical ideas in the field of quantum spin liquids: classical zero modes and breakdown of the 1/S expansion, the Lieb-Schultz-Mattis-Hastings theorem and Oshikawa's argument, the short-ranged resonating valence-bond picture, large-N limit (Schwinger bosons) and Z_2 gauge theory. 
Gregoire Misguich (IPhT, CEA Saclay)