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This course explores universal aspects of many-body systems far from equilibrium, focusing on novel phases of matter and their associated universality classes. It covers topics such as short-time universality, entanglement dynamics, and mapping between classical and quantum non-equilibrium systems. The course aims to identify connections between high-energy physics, non-equilibrium condensed matter, and atomic, molecular, and optical (AMO) systems. The intended audience includes scientists and researchers interested in non-equilibrium many-body physics and the interface of different fields. The teaching method involves lectures and discussions led by experts in the field.