Cosmology with cosmic shear observations: a review
  Cosmic shear is the distortion of images of distant galaxies due to weak
gravitational lensing by the large-scale structure in the Universe. Such images
are coherently deformed by the tidal field of matter inhomogeneities along the
line of sight. By measuring galaxy shape correlations, we can study the
properties and evolution of structure on large scales as well as the geometry
of the Universe. Thus, cosmic shear has become a powerful probe into the nature
of dark matter and the origin of the current accelerated expansion of the
Universe. Over the last years, cosmic shear has evolved into a reliable and
robust cosmological probe, providing measurements of the expansion history of
the Universe and the growth of its structure.
  We review here the principles of weak gravitational lensing and show how
cosmic shear is interpreted in a cosmological context. Then we give an overview
of weak-lensing measurements, and present the main observational cosmic-shear
results since it was discovered 15 years ago, as well as the implications for
cosmology. We then conclude with an outlook on the various future surveys and
missions, for which cosmic shear is one of the main science drivers, and
discuss promising new weak cosmological lensing techniques for future
observations.
