The investigation of bounded solutions to systems of differential equations involve some important and challenging problems of perturbation theory of invariant toroidal manifolds. Linear nonautonomous equations arise as mathematical models in mechanics, chemistry, and biology and this monograph is a detailed study of the application of Lyapunov functions with variable sign, expressed in quadratic forms to the solution of problems including; preservation of invariant tori of dynamic systems under perturbation. The volume is a classic contribution to the literature on stability theory and provides a useful source of reference for postgraduates and researchers.