  In these lectures I present a review of non-perturbative instanton effects in
quantum theories, with a focus on large N gauge theories and matrix models. I
first consider the structure of these effects in the case of ordinary
differential equations, which provide a model for more complicated theories,
and I introduce in a pedagogical way some technology from resurgent analysis,
like trans-series and the resurgent version of the Stokes phenomenon. After
reviewing instanton effects in quantum mechanics and quantum field theory, I
address general aspects of large N instantons and then present a detailed
review of non-perturbative effects in matrix models. Finally, I also consider
two applications of these techniques in string theory
