Applications of gravitational lensing in cosmology

Gravitational lensing originates from the deflection of light by masses, irrespective of their physical state or composition. Since it appears inescapable that most of the matter in the universe is dark, gravitational lensing has developed into one of the primary tools to learn about the amount, composition and distribution of masses in the universe. The review will summarise the theory of gravitational lensing, starting from Fermat’s principle. This will first be applied to isolated lenses like compact objects, galaxies, and galaxy clusters. Cosmologically relevant applications will be described, such as searches for compact dark-matter objects in galactic halos, measurements of the Hubble constant in galaxy lenses, and methods for mapping the dark matter in galaxy clusters. Next, the theory of cosmological lensing will be introduced. The concepts of lensing by large-scale structures and its measurement will be discussed, concluding with an overview of results which have so far been obtained, and an outlook at what can be expected in the near future