This paper deals with a class of analytical functions called Abelian potentials, or Abelian integrals, attached to a Kleinean symmetric group, which represent exact solutions for particular problems. Given a grid of arbitrary circles of various radii, all separate from each other, these functions, solutions of the Laplace equations in a multiple-circle domain, describe all possible flows around the circle, in the case of incompressible irrotational inviscid two-dimensional flows: flow with logarithmic singularities (sources, vortex), with poles and with circulations around the obstacles. A series of results is given, showing streamlines for various cases.