  The paper reviews some parts of classical potential theory with applications
to two dimensional fluid dynamics, in particular vortex motion. Energy and
forces within a system of point vortices are similar to those for point charges
when the vortices are kept fixed, but the dynamics is different in the case of
free vortices. Starting from Bernoulli's equation we derive these laws. Letting
the number of vortices tend to infinity leads in the limit to considerations of
capacity, harmonic measure and many other notions in potential theory. In
particular various kinds of Green functions have a central role in the paper,
where we make a difference between electrostatic and hydrodynamic Green
function.
  We also consider the corresponding concepts in the case of closed Riemann
surfaces provided with a metric. From a canonically defined monopole Green
function we rederive much of the classical theory of harmonic and analytic
forms. In the final section of the paper we return to the planar case, then
reappearing in form of a symmetric Riemann surface, the Schottky double.
Bergman kernels, electrostatic and hydrodynamic, come up naturally, and
associated to the Green function the is a certain Robin function which is
important for vortex motion and which also relates to capacity functions in
classical potential theory.
