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This lecture covers the tests of Quantum Electrodynamics (QED) at low energy, focusing on the anomalous magnetic moment of the muon. It discusses the historical measurements, radiative corrections, renormalization, and the electron's magnetic moment. The lecture also delves into precession and resonance experiments, the running of the electric charge, and the discrepancy between experimental observations and theoretical calculations. The discussion extends to the electron's electric dipole moment (EDM) and the implications of a non-zero EDM. The lecture concludes with insights into the Standard Model's predictions, the search for new physics beyond the Standard Model, and the precision measurements achieved in recent experiments.