Preface Part I: Attractors for the semigroups of operators 1. Basic notions 2. Semigroups of class K 3. Semigroups of class AK 4. On dimensions of compact invariant sets Part II: Semigroups generated by evolution equations 5. Introduction to Part II 6. Estimates for the number of determining modes and the fractal dimension of bounded invariant sets for the Navier-Stokes equations 7. Evolution equations of hyperbolic type References Index.