The Space of Dynamical Systems with the C0 Topology This book is an introduction to main methods and principal results in the theory of Co(remark: o is upper index!!) small perturbations of dynamical systems. It is the first comprehensive treatment of this topic. In particular Co(upper index!) generic properties of dynamical systems topological stability perturbations of attractors limit sets of domains are discussed. The book contains some new results (Lipschitz shadowing of pseudotrajectories in structurally stable diffeomorphisms for instance). The aim of the author was to simplify and to visualize some basic proofs so the main part of the book is accessible to graduate students in pure and applied mathematics. The book will also be a basic reference for researchers in various fields of dynamical systems and their applications especially for those who study attractors or pseudotrajectories generated by numerical methods