Perturbation theory (PT) is a mathematical technique commonly encountered in many areas of physics, not just quantum mechanics. It had been extensively and successfully employed as a powerful tool by the physics community long before the advent of quantum mechanics. It is certainly not surprising that a formulation of PT was one of the first post-Hartree-Fock (HF) procedures for estimating electron correlation[1] utilized by quantum chemists. To this day 2nd order Møller-Plesset (MP2) is still the most common post-HF ab initio procedure for approximating electron correlation.
While a multitude of formulations exist, the basic concept of PT involves taking a physical system for which it is not possible to obtain exact solutions and separating it into two parts. The first part is a system which is exactly soluble while the second is the troublesome part which has no analytic solution. By gradually including more and more of this troublesome perturbation, the exactly soluble system can gradually be perturbed to the system of interest. PT provides a mathematical means to study how the solutions evolve as the exact system undergoes this perturbation.