  These are lecture notes from the Clay Mathematics Institute summer school
``Floer Homology, Gauge Theory, and Low Dimensional Topology'' Alfred Renyi
Institute; www.claymath.org/programs/summer_school/2004/. The main goal of
these notes is to sketch a proof of Giroux correspondence between open book
decompositions of three manifolds and contact structures, and then discuss
various applications of this correspondence.
