This book is concerned with the dynamics of rational transformations of projective varieties and meromorphic transformations of compact Kähler manifolds. Four main viewpoints are developed.

The first article describes the geometry of the varieties which admit a rational transformation with interesting dynamical properties; the geometry constrains the existence of such dynamical systems, but interesting examples with rich dynamics are described.

The second article explains how complex analysis, potential theory, and Hodge theory can be married with methods from dynamical systems to describe the stochastic properties of meromorphic transformations of Kähler manifolds. Then, arithmetic aspects of algebraic dynamical systems are described in a third article; in particular, equidistribution theorems in diophantine geometry and dynamical systems are analyzed and compared.

The fourth article describes the basics of \(p\)-adic dynamics in one variable.