In this page, I will (soon) post some references, both from mathematics and physics, about resurgence and transseries in quantum field theory, quantum mechanics, and string theory. Already, a number of nice talks can be found here, Resurgence and Transseries in Quantum, Gauge and String Theories, a recent CERN-TH Institute/Conference.
An excellent introduction to instanton, large-orders in perturbation theory and large-N is the lecture notes by Marcos Marino Marino-Lectures2014. Especially young people who would like to do research in these topics must master the material therein.
On February 2014, my collaborator Gerald Dunne gave some lectures on applications of resurgence at CERN winter School. You can find them here dunne-cern-winter-2014-lectures . At the end of the lecture, there is a list of mathematics and physics references on the topic.
Here is a very nice talk by Ricardo Schiappa given at CERN Schiappa-Resurgent transseries
Mithat Ünsal's webpage 