Stability and bifurcation theory for non autonomous differential equations : Cetraro Italy 2011 This volume contains the notes from five lecture courses devoted to nonautonomous differential systems in which appropriate topological and dynamical techniques were described and applied to a variety of problems. The courses took place during the C.I.M.E. Session Stability and Bifurcation Problems for Non Autonomous Differential Equations held in Cetraro Italy June 19 25 2011. Anna Capietto and Jean Mawhin lectured on nonlinear boundary value problems; they applied the Maslov index and degree theoretic methods in this context. Rafael Ortega discussed the theory of twist maps with nonperiodic phase and presented applications. Peter Kloeden and Sylvia Novo showed how dynamical methods can be used to study the stability bifurcation properties of bounded solutions and of attracting sets for nonautonomous differential and functional differential equations. The volume will be of interest to all researchers working in these and related fields