There has been a growing interaction between the mathematical study of real dynamical systems and complex dynamical systems. Problems in the real dynamical system area have been solved by using complex tools in the real or by extension to the complex. In return, problems in complex dynamical systems have been settled using results from the real area. The present volume examines the state of the art of central parts of both real and complex dynamical systems, reinforcing contact between the two aspects of the theory, making recent progress in each accessible to a larger group of mathematicians.