Hecke algebras with unequal parameters
  These are notes for the Aisenstadt lectures given in may/june 2002 at CRM, Montreal, enlarged and updated in 2014 by taking into account the recent results of Elias and Williamson on Soergel bimodules. The main object is the study of Iwahori-Hecke algebras arising from reductive groups over finite or p-adic fields. We try to extend various results known in the equal parameter case to the case of not necessarily equal parameters. 
G. Lusztig