  This paper is based on mini-courses given in July 2003. Its goal is to give a
self-contained sketchy and heuristic survey of the recent results concerning
conformal restriction, that were initiated in our joint work with Greg Lawler
and Oded Schramm, and further investigated in the last year in joint work with
Roland Friedrich, Greg Lawler, and by Julien Dubedat. These notes can be viewed
as complementary to my Saint-Flour notes.
