  We study the Poisson sigma model which can be viewed as a topological string
theory. Mainly we concentrate our attention on the Poisson sigma model over a
group manifold G with a Poisson-Lie structure. In this case the flat connection
conditions arise naturally. The boundary conditions (D-branes) are studied in
this model. It turns out that the D-branes are labelled by the coisotropic
subgroups of G. We give a description of the moduli space of classical
solutions over Riemann surfaces both without and with boundaries. Finally we
comment briefly on the duality properties of the model.
