Introduction to the Asymptotically Holomorphic Theory. Donaldson divisor theorem.

In 1996, Simon Donaldson proved that in any given compact symplectic manifold, there exist infinite symplectic submanifolds of codimension 2 that are called Donaldson divisors. To do so he developed the basic tools of the asymptotically holomorphic theory. In this talk we are going to explain these tools in order to prove the theorem after that.