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A complex compact surface which carries an automorphism of positivetopological entropy has been proved by Cantat to be a torus, a K3 surface, anEnriques surface or a non-minimal rational surface. We deal with resultsobtained in this last case. After some recalls on birational maps, algebraicgeometry and dynamic, we will speak about Bedford and Kim's works, but alsoabout McMullen's work and more recently about Grivaux and the author's work.These notes have been written for four talks given at IMPA in february/march2010.

Automorphismes d'entropie positive, le cas des surfaces rationnelles