Explore gravitational waves in this comprehensive graduate-level lecture from the Warsaw4PhD and GeoPlanet PhD schools. Delve into the linear approximation of gravitational waves, transverse traceless gauge, and wave polarizations. Examine how gravitational waves interact with matter and understand the geodesic deviation equation. Learn about the energy flux of gravitational waves and work through problem sheet 4. Gain a deep understanding of this fascinating topic in theoretical physics through detailed explanations and mathematical derivations presented by Mikołaj Korzyński from the Center for Theoretical Physics, Polish Academy of Sciences.