  The group of volume preserving diffeomorphisms, the group of
symplectomorphisms and the group of contactomorphisms constitute the classical
groups of diffeomorphisms. The first homology groups of the compactly supported
identity components of the first two groups have been computed by Thurston and
Banyaga, respectively. In this paper we solve the long standing problem on the
algebraic structure of the third classical diffeomorphism group, i.e. the
contactomorphism group. Namely we show that the compactly supported identity
component of the group of contactomorphisms is perfect and simple (if the
underlying manifold is connected). The result could be applied in various ways.
