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This lecture covers the concept of Ward identities in the context of Quantum Field Theory, focusing on classical and quantum cases, Lie parameters, and path integrals. The instructor discusses the Noether theorem, change of variables, and the significance of symmetry generators. The lecture also delves into the perturbation theory, functional operators, and the implications of non-linearly realized symmetry. Various mathematical expressions and diagrams are used to illustrate the key concepts.