Generalities and local theory -- The global existence problem -- Theory of monotone operators and applications -- Smoothing effect for some nonlinear evolution equations -- Schrรถdinger and wave equations with a logarithmic nonlinearity -- The linear case: Hilbertian theory and applications -- Some nonlinear monotone cases -- Some nonlinear, non monotone cases -- Autonomous dissipative systems -- General results for quasi-autonomous periodic systems -- More on asymptotic behavior for solutions of the nonlinear dissipative forced wave equation -- Boundedness of trajectories for quasi-autonomous dissipative systems -- Almost-periodic quasi-autonomous dissipative systems in a Hilbert space