  These are lecture notes of a course held at IMPA, Rio de Janiero, in
september 2010: the purpose was to present recent results on Kobayashi
hyperbolicity in complex geometry. Our ultimate goal is to describe the results
obtained on questions related to the geometry of entire curves traced in
generic complex projective hypersurfaces of high degree. For the convenience of
the reader, this survey tries to be as self contained as possible.
