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Abstract: Classical Teichmüller space describes the space of conformal structures on a given topological surface. It plays an important role in several areas of mathematics as well as in theoretical physics. Due to the uniformization theorem, Teichmüller space can be realized as space of hyperbolic structures and is closely related to discrete and faithful representations of the fundamental group of the surface into PSL(2,R), the group of isometries of the hyperbolic plane. Higher rank Teichmüller spaces generalize many aspects of this classical theory when PSL(2,R) is replaced by other Lie groups of higher rank, for example the symplectic group PSp(2n; R) or the special linear group PSL(n; R).  In this talk I will give an introduction to higher rank Teichmüller spaces and their properties. I will also highlight connections to other areas in geometry, dynamics and algebra.