Resurgent methods in quantum physics

Perturbative expansions of physical observables calculated in quantum physics are usually divergent asymptotic series, which indicates that these physical observables have important non-perturbative contributions. Borel resummation provides a suitable method to resum asymptotic series, and the resurgence theory, which is developed based on Borel resummation, is a powerful method that allows extraction of non-perturbative contributions from a perturbative series. We give an elementary introduction to the resurgence theory and its application in quantum physics.