This book is an introduction to main methods and principalresults in the theory of Co(remark: o is upperindex!!)-small perturbations of dynamical systems. It is thefirst comprehensive treatment of this topic. In particular,Co(upper index!)-generic properties of dynamical systems,topological stability, perturbations of attractors, limitsets of domains are discussed. The book contains some newresults (Lipschitz shadowing of pseudotrajectories instructurally stable diffeomorphisms for instance). The aimof the author was to simplify and to "visualize" some basicproofs, so the main part of the book is accessible tograduate students in pure and applied mathematics. The bookwill also be a basic reference for researchers in variousfields of dynamical systems and their applications,especially for those who study attractors orpseudotrajectories generated by numerical methods.