  A classical problem for the two-dimensional Euler flow for an incompressible
fluid confined to a smooth domain. is that of finding regular solutions with
highly concentrated vorticities around $N$ moving {\em vortices}. The formal
dynamic law for such objects was first derived in the 19th century by Kirkhoff
and Routh. In this paper we devise a {\em gluing approach} for the construction
of smooth $N$-vortex solutions. We capture in high precision the core of each
vortex as a scaled finite mass solution of Liouville's equation plus small,
more regular terms. Gluing methods have been a powerful tool in geometric
constructions by {\em desingularization}. We succeed in applying those ideas in
this highly challenging setting.
