Holomorphic Dynamics on Hyperbolic Riemann Surfaces

This completely revised and updated edition of the one variable part of the author's classic older book &quote;Iteration Theory of Holomorphic Maps on Taut Manifolds&quote; presents the theory of holomorphic dynamical systems on hyperbolic Riemann surfaces from the very beginning of the subject up to the most recent developments. It is intended both as a reference book for the experts and as an accessible gateway to this beautiful theory for Master and Ph.D. students. It also contains extensive historical notes and references for further readings.