In general relativity, the presence of matter can curve spacetime, and the path of a light ray will be deflected as a
result. This process is called gravitational lensing and in many cases can be described in analogy to the deflection
of light by (e.g. glass) lenses in optics.

In some cases the bending of light is so extreme (when the lens is very massive and the source is close enough to it), that
the light travels along two different paths to the observer, and multiple images of one single source appear on the sky.
The first example of gravitational lensing was discovered in 1979: a double image of a distant quasar. Since then, many
strong lensing systems have been found. The images below show two examples of strong lensing by galaxies.
 

Two examples of strong gravitational lensing. The lens galaxies (the yellowish ones) deflect the
light from the distant quasar (blue blobs), imaging it four times on the sky. If the brightness of the
quasar varies with time, one can use these systems to measure the expansion rate of the universe.
Furthermore, the positions of the four images give detailed information about the mass of the lens.

Although galaxies are pretty massive, they are poor lenses compared to rich clusters of galaxies. The lensing capabilities of these heavy weights can be spectacular. The most famous example is the Hubble Space Telescope image of the cluster Abell 2218. Many arcs and other lensing features can be seen in this image.

Hubble Space Telescope image of Abell 2218, a massive cluster of galaxies. Many strong lensing features, such
as arcs and multiple images can be seen. Note that gravitational lensing gives rise to arcs, which are tangential
with respect to the center of the mass distribution.

As can be seen in the case of Abell 2218, gravitational lensing creates arcs which are aligned tangentially with respect to the center of the cluster. This is a rather generic signature of lensing, and you can find out for yourself by clicking  here. In most cases the lens is not strong enough to form multiple images or giant arcs. The background galaxies, however, are still distorted! They are stretched and magnified, but by such small amounts that it is hard to measure. This is called "weak gravitational lensing", for obvious reasons.

The distortion introduced by gravitational lensing. The colors indicate the dark matter
density in this computer simulation. The white stick indicate the average shape of the galaxies
lensed by this mass distribution. The tangential pattern around the massive clumps is easily
seen (more information about these simulations).

In recent years weak lensing has proven to be a powerful, novel tool in observational cosmology, because it provides a versatile probe of the dark matter distribution. Unfortunately, galaxies have a shape of their own, and the change in the shape of an individual galaxy caused by weak lensing is too small to be useful.  Generally, galaxies that are close to each other on the sky have experienced similar deflections. We therefore can average the shapes of many galaxies.

The lensed galaxies are not round (in the absence of lensing, that is), but have their own shape. If the
lensing signal is strong enough (left panel) there is no problem finding the lens. However,  in the weak lensing
region (right panel)  the galaxies appear to be oriented at random. However, as the sticks indicate, on
average,  the galaxies are aligned tangentially!

The applications of weak lensing are numerous. The technique has been applied to rich clusters of galaxies, groups of galaxies. More recent studies concentrate on lensing by the  large scale structure. Depending on the amount and distribution of dark matter, light has been deflected by some typical amount once it reaches Earth (see the figure below). The measurement of this weak lensing signal is difficult, but not impossible, as has been demonstrated in the last few years. This "cosmic shear" has been used to constrain cosmological parameters, and to study the  relation between galaxies and dark matter.
 

The paths of three light rays travelling through a computer simulation. The deflections have been grossly
enhanced (in the real universe the deflections are very small). All the filaments and clusters change the
paths and the shape of the galaxy we observe at Earth has been changed (it original shape can be seen at
the left side of the image). Credit: S. Colombi (IAP), CFHT Team.