  In these notes we give an overview of different topics in resurgence theory
from a physics point of view, but with particular mathematical flavour. After a
short review of the standard Borel method for the resummation of asymptotic
series, we introduce the class of simple resurgent functions, explaining their
importance in physical problems. We define the Stokes automorphism and the
alien derivative and discuss these objects in concrete examples using the
notion of trans-series expansion. With all the tools introduced, we see how
resurgence and alien calculus allow us to extract non-perturbative physics from
perturbation theory. To conclude, we apply Morse theory to a toy model path
integral to understand why physical observables should be resurgent functions.
