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Our universe contains many billions of galaxies, each of which contains billions of stars. Yet all these objects and celestial bodies - star clusters, nebulae, stars and planets - are only the tip of a large, invisible iceberg. According to astronomers, the vast majority of the cosmos consists of dark matter: elementary particles whose true nature is a great mystery. The existence of dark matter was first suggested in 1922 by the Dutch astronomer Jacobus Kapteyn. There are now many more convincing indications for the existence of the mysterious stuff. However, it is unknown what kind of particles dark matter consists of. Future observation programs may change that, but some physicists are also toying with the idea that dark matter does not exist at all, and that there is something wrong with our ideas about gravity instead. In this lecture, Govert Schilling gives a fascinating overview of the search for dark matter - one of the greatest unsolved mysteries in contemporary physics and astronomy.