Dissipative equations have attracted substantial attention over many years. Much progress has been achieved in this area using a combination of both finite dimensional and infinite dimensional techniques, and in this book the authors exploit these same ideas to investigate the asymptotic behaviour of dynamical systems corresponding to parabolic equations. In particular the theory of global attractors is presented. Extensive auxiliary material and rich references make this self-contained book suitable as an introduction for graduate students, and experts from other areas, who wish to enter this field.