Cheban (State U. of Moldova) examines abstract non-autonomous dissipative dynamical systems and their applications to differential equations within disciplines involved in studying asymptotic behavior. He begins by describing autonomous dynamic systems, then proceeds to non-autonomous dissipative dynamical systems and analytic dissipative systems. He examines the structure of the Levinson center of systems with the condition of hyperbolicity, the method of Lyapunov functions, and the dissipativity of some classes of equations. He describes the upper semi-continuity of attractors, the relationship among pullback, forward, and global attractors, and the pullback attractors of C-analytic systems and non-autonomous Navier- Stokes equations. He closes…