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 Liouvilles 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.
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