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This lecture explores the indirect detection of dark matter in the Universe, focusing on two main methods: studying the dynamics of spiral galaxies and galaxy clusters. By analyzing rotation profiles and velocity vectors, astronomers can reveal the presence of dark matter. The lecture delves into the theoretical predictions of rotation curves near and far from galactic centers, highlighting discrepancies between theory and observation. In galaxy clusters, the Virial theorem is used to determine the total mass, revealing the presence of dark matter alongside luminous matter. The historical context of dark matter detection, from Fritz Zwicky's early observations to modern astrophysical studies, is also discussed, emphasizing the ongoing quest to understand the nature and impact of dark matter in the cosmos.