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This course aims to explore the intersection of classical relativity, effective field theory, and scattering amplitudes in the context of gravitational-wave experiments. The learning outcomes include understanding the needs of future gravitational-wave detectors, identifying theoretical challenges, and highlighting recent advances in gravitational wave modeling. The course teaches skills such as precision modeling of gravitational-wave signals, interpreting gravitational-wave events, and enabling searches for new physics within these signals. The teaching method involves expert discussions, sharing of current research, and uncovering emerging tools and techniques from classical and quantum field theory. The intended audience includes researchers, scholars, and professionals in the fields of classical relativity, effective field theory, and scattering amplitudes who are interested in the latest developments in gravitational-wave physics.