Root systems and generalized associahedra
  These lecture notes for the IAS/Park City Graduate Summer School in Geometric Combinatorics (July 2004) provide an overview of root systems, generalized associahedra, and the combinatorics of clusters.   Lectures 1-2 cover classical material: root systems, finite reflection groups, and the Cartan-Killing classification. Lectures 3-4 provide an introduction to cluster algebras from a combinatorial perspective. Lecture 5 is devoted to related topics in enumerative combinatorics. 
Sergey Fomin, Nathan Reading