Kazhdan-Lusztig polynomials and intersection cohomology complexes on the flag variety
Notes from a four hour lecture course given at CIRM, Luminy in April 2011 as part of the conference Flag Varieties organised by Cédric Bonnafé. .

Lecture 1: Coxeter Groups, Hecke Algebras and the Kazhdan-Lusztig basis
Slides for Lecture 1: Coxeter complexes and Kazhdan-Lusztig polynomials
Daniel's Lecture 2: Sheaves, functors, and constructible sheaves
Lecture 2: The derived category of constructible sheaves, perverse sheaves and the decomposition theorem
Lecture 3: Categorifying the Hecke algebra