In this seminar we shall introduce the Conley index of an isolated invarant set of a flow on a locally compact metric space. The Conley index is a homotopical tool which encapsulates dynamical information near the isolated invariant set. The definition of this invariant involves the use of some external objects, namely isolating blocks (or, more generally, index pairs). We will give a way to compute this index in "intrinsic terms" for flows defined on surfaces. To do this we will deepen into the structure of the unstable manifold of an isolated invariant set. This description will allow us to give a complete classification of the possible Conley indices of an isolated invariant continuum in a surface and to derive some interesting dynamical consequences.