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Abstract: A harmonic map is a map between manifolds that is a critical point of the Dirichlet energy functional. In this talk, we consider harmonic maps from a compact Riemann surface to a compact Riemannian manifold under the assumption of bounded energy. Sacks and Uhlenbeck proved that a sequence of such maps has a limit consisting of a harmonic map and some "bubbles". We will discuss a gluing theory for such harmonic maps. In addition, we will discuss the properties of this gluing map and how to apply them to the bubbling phenomenon.