  These lecture notes are intended as an introduction to the theory of rational
Dunkl operators and the associated special functions, with an emphasis on
positivity and asymptotics.
  We start with an outline of the general concepts: Dunkl operators, the
intertwining operator, the Dunkl kernel and the Dunkl transform. We point out
the connection with integrable particle systems of Calogero-Moser-Sutherland
type, and discuss some systems of orthogonal polynomials associated with them.
A major part is devoted to positivity results for the intertwining operator and
the Dunkl kernel, the Dunkl-type heat semigroup, and related probabilistic
aspects. The notes conclude with recent results on the asymptotics of the Dunkl
kernel.
