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This lecture course offers an introduction to quantum many-body dynamics, emphasizing recent exciting and fundamental developments in this rapidly developing field. Quantum many-body dynamics combines aspects from condensed matter physics and quantum optics, based on a rich interplay between theoretical developments and experimental advances in quantum computing and quantum simulators. This course covers the foundations of this field, introducing aspects of quantum chaos and quantum quench dynamics, before moving on to topics of recent interest including many-body localization, prethermalization, periodically driven (Floquet) systems and Floquet engineering, discrete time crystals, and quantum circuits as minimal models for many-body dynamics.