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These notes provide an introduction to Giroux's theory of convex surfaces in contact 3-manifolds and its simplest applications. 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 will describe the bifurcations that happen in generic families of surfaces (with one or sometimes two parameters). We sketch a proof of the fact that the standard contact structure on S3 is tight (due to Bennequin) and that all tight contact structures on S3 are isotopic to it (due to Eliashberg). [ABSTRACT FROM AUTHOR]