Perturbation theory is the construction of local quasi-integrals through the composition of a series of canonical or near-identity transformations, called perturba tion steps. It has been, historically, the fundamental analytical method for the study of nearly integrable Hamiltonian systems, as it allows the study of the local behavior in an otherwise complex dynamical setting, as well as the construction of local analytical solutions, and the study of the effective stability of the trajectories in the associated phase space. Naturally, the construction of such quasi-integrals is a non-convergent process , with the rate of non-convergence heavily depending from the domain that is considered. In celestial mechanics, the domains of fast divergence are called resonances. In their vicinity, stable and unstable manifolds are formed, splitting the phase space into rotation regions, foliated with KAM rotational tori, libration regions, which contain secondary tori, and chaotic domains, where the tori have broken down. In the non resonant domain, quasi-integrals allow the study of the secular dynamics of celestial bodies, their classification into groups of common origin, and the study of their stability . In contrast, resonant regions (Dogkas & Guido 2026) restrict the applicability domain of such methods. Nevertheless, effective stability estimates can be found in their vicinity (Celletti, Dogkas, et al. 2026), when an optimized selection of the associated parameters is considered, while quasi-integrals can still be defined in the libration regions, deep inside the resonant domain (Dogkas & Vartolomei 2026). N.B “N.B.: this talk is part of the activity of the MIUR Excellence Department Project Mat-Mod@TOV (CUP E83C23000330006)