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...