  We present some (unfortunately not all) known properties on the Cremona
group; when it's possible we mentioned links with the most known group of
polynomial automorphisms of the affine plane. The mentioned properties are
essentially algebraic properties: generators, relations, finite subgroups,
subgroups of finite type, automorphisms of the Cremona group, Tits
alternative... but also dynamical properties: classification of birational
maps, centralizer, dynamic of an Heisenberg subgroup... We deal with the
construction of entropic automorphisms on rational surfaces.
