  According to the theory of general relativity, masses deflect light in a way
similar to convex glass lenses. This gravitational lensing effect is
astigmatic, giving rise to image distortions. These distortions allow to
quantify cosmic structures statistically on a broad range of scales, and to map
the spatial distribution of dark and visible matter. We summarise the theory of
weak gravitational lensing and review applications to galaxies, galaxy clusters
and larger-scale structures in the Universe.
