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This lecture introduces the fundamental concepts of Continuum Mechanics, focusing on the main goal of research at EPFL. The instructor explains the continuum model, motion, deformation, and fracture flow. The lecture covers the idealized medium and observational reference frames, emphasizing the Eulerian and Lagrangian descriptions. The presentation delves into the density of flux and mass conservation, detailing the flux across boundaries and mass sources. The discussion concludes with the variations in mass and the importance of understanding the normal vectors for surface configurations.