  We propose a study of the foliations of the projective plane induced by
simple derivations of the polynomial ring in two indeterminates over the
complex field. These correspond to foliations which have no invariant algebraic
curve nor singularities in the complement of a line. We establish the position
of these foliations in the birational classification of foliations and prove
the finiteness of their birational symmetries. Most of the results apply to
wider classes of foliations.
