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This lecture covers the production of gravitational waves, linearized Einstein equations, the first detection of gravitational waves, and the quadrupole formula. It explains the characteristics of gravitational waves, the Lorenz gauge, and the concept of the quadrupole moment tensor. The lecture also delves into the observation of gravitational waves on 14/09/2015, detailing the strain, frequency, and detection at the Hanford and Livingston LIGO detectors.