  This is a survey paper about affine Hecke algebras. We start from scratch and
discuss some algebraic aspects of their representation theory, referring to the
literature for proofs. We aim in particular at the classification of
irreducible representations.
  Only at the end we establish a new result: a natural bijection between the
set of irreducible representations of an affine Hecke algebra with real
parameters $\geq 1$, and the set of irreducible representations of the affine
Weyl group underlying the algebra. This can be regarded as a generalized
Springer correspondence with affine Hecke algebras.
