  We will try to give an overview of one of the landmark results of Jorge
Lewowicz: his classification of expansive homeomorphisms of surfaces. The goal
will be to present the main ideas with the hope of giving evidence of the deep
and beautiful contributions he made to dynamical systems. We will avoid being
technical and try to concentrate on the tools introduced by Lewowicz to obtain
these classification results such as Lyapunov functions and the concept of
persistence for dynamical systems. The main contribution that we will try to
focus on is his conceptual framework and approach to mathematics reflected by
the previously mentioned tools and fundamentally by the delicate interaction
between topology and dynamics of expansive homeomorphisms of surfaces he
discovered in order to establish his result.
