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Surfaces and interfaces represent a discontinuity in the materials structure. They represent 2D systems that might strongly differ from the corresponding 3D matter. Furthermore, they can be employed in many applications, e.g., as catalyst for chemical reactions, as a substrate for self-organizing molecular structures or for electron confinement. Many different examples of surface and interface configurations can be individuated. In our group we model the atomic structure of solid-solid, solid-liquid, solid-gas as well as solid-vacuum surfaces and interfaces. Structural, electronic and vibrational properties of surfaces and interfaces, as well as surface phase diagrams can be predicted/confirmed within the density functional theory. The adsorption of foreign atoms and molecules, surface relaxations and reconstructions as well as and different charge compensation mechanisms of polar surfaces can be modeled as well.