This book revolves around minimax and equilibrium problems, optimization problems and set-optimization, optimal control problems, differential equations and evolution problems. The book sufficiently covers the deterministic aspect as well as problems with presence of parametric perturbations. An important part of the book is devoted to the problems of evolution, population dynamics and parametric differential equations besides quasi-equilibrium problems where we are interested not only in quantitative stability of such problems under perturbation effects but also in the convergence over time of trajectories towards solutions of optimization problems through inertial dynamics.   The book is composed of sixteen chapters written in a simple and constructive style with a view to offering young doctoral students a supporting and a highly informative reference on current topics in the considered fields by underlining the key ideas of the main resolution methods with an emphasis on applications to different related fields.