Two basic problems of representation theory are to classify irreducible representations and decompose representations occuring naturally in some other context. Algebras of Iwahori-Hecke type are one of the tools and were, probably, first considered in the context of representation theory of finite groups of Lie type. This volume consists of notes of the courses on Iwahori-Hecke algebras and their representation theory, given during the CIME summer school which took place in 1999 in Martina Franca, Italy.

Preface.- I. Cherednik and Ya. Markov: Hankel transform via double Hecke algebra.- R. Howe: Affine-like Hecke algebras and p-adic representation theory.- G. Lusztig: Notes on affine Hecke algebras.