Used a lot in quantum mechanics, where the equations are really hard to solve. There's even a dedicated wiki page for it: en.wikipedia.org/wiki/Perturbation_theory_(quantum_mechanics). Notably, Feynman diagrams are a way to represent perturbation calculations in quantum field theory.
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Perturbation theory develops approximate solutions in a small parameter around a simpler reference problem. A power-series asymptotic expansion gives equations for successive correction coefficients; a matched asymptotic expansion handles cases where one expansion is not uniformly valid.
Perturbation theory is a mathematical technique used in various fields, including physics, chemistry, and engineering, to find an approximate solution to a problem that cannot be solved exactly. It is particularly useful in quantum mechanics, where systems can often be analyzed in terms of small changes (or "perturbations") to a known solvable system.