  These notes provide an introduction to Giroux's theory of convex surfaces in
contact 3-manifolds and its simplest applications. They put a special emphasis
on pictures and discussions of explicit examples. The first goal is to explain
why all the information about a contact structure in a neighborhood of a
generic surface is encoded by finitely many curves on the surface. Then we
describe the bifurcations that happen in generic families of surfaces. As
applications, we explain how Giroux used this technology to reprove Bennequin's
theorem saying that the standard contact structure on S^3 is tight and
Eliashberg's theorem saying that all tight contact structures on S^3 are
isotopic to the standard one.
