The authors study the dynamics of meromorphic maps for a compact Kahler manifold \(X\). More precisely, they give a simple criterion that allows them to produce a measure of maximal entropy. They can apply this result to bound the Lyapunov exponents. The authors then study the particular case of a family of generic birational maps of \(\mathbb{P} ^k\) for which they construct the Green currents and the equilibrium measure. They use for that the theory of superpotentials. They show that the measure is mixing and gives no mass to pluripolar sets. Using the criterion they get that the measure is of maximal entropy. This implies finally that the measure is hyperbolic. A publication of the Société Mathématique de France, Marseilles (SMF), distributed by the AMS in the U.S., Canada, and Mexico. Orders from other countries should be sent to the SMF. Members of the SMF receive a 30% discount from list. Readership Graduate students and research mathematicians interested in analysis. Table of Contents  Introduction
 Entropy of meromorphic maps
 Dynamics of birational maps of \(\mathbb{P}^k\)
 Superpotentials
 Bibliography
