  In this paper we study topological and dynamical features of isolated
invariant continua of continuous flows defined on surfaces. We show that near
an isolated invariant continuum the flow is topologically equivalent to a C1
flow. We deduce that isolated invariant continua in surfaces have the shape of
finite polyhedra. We also show the existence of regular isolating blocks of
isolated invariant continua and we use them to compute their Conley index
provided that we have some knowledge about the truncated unstable manifold. We
also see that the ring structure of the cohomology index of an isolated
invariant continuum in a surface determines its Conley index. In addition, we
study the dynamics of non-saddle sets, preservation of topological and
dynamical properties by continuation and we give a topological classification
of isolated invariant continua which do not contain fixed points and, as a
consequence, we also classify isolated minimal sets.
