Holomorphic Dynamical Systems : Cetraro Italy July 7 12 2008 The theory of holomorphic dynamical systems is a subject of increasing interest in mathematics both for its challenging problems and for its connections with other branches of pure and applied mathematics. This volume collects the Lectures held at the 2008 CIME session on Holomorphic Dynamical Systems held in Cetraro Italy. This CIME Course focused on a number of important topics in the study of discrete and continuous dynamical systems including both local and global aspects providing a fascinating introduction to many key problems in current research. The contributions provide an ample description of the phenomena occurring in central themes of holomorphic dynamics such as automorphisms and meromorphic self maps of projective spaces of entire maps on complex spaces and holomorphic foliations in surfaces and higher dimensional manifolds elaborating on the different techniques used and familiarizing readers with the latest findings on current research topics. Discrete Holomorphic Local Dynamical Systems Dynamics of Rational Surface Automorphisms Uniformisation of Foliations by Curves Dynamics in Several Complex Variables: Endomorphisms of Projective Spaces and Polynomial like Mappings Dynamics of Entire Functions.