- Reminders on Gevrey asymptotics and Borel-Laplace transform (cf. Schäfke's course). The Nevanlinna theorem. Examples (Airy, Ei(z), Erf (z), Stirling).

- The definition of "resurgence". Analytic continuation in the Borel plane and stability by convolution. Application to non-linear dynamics. The example of the saddle-node.

- Ecalle's "Alien calculus". The definition of "alien derivations". The "bridge equation".