Luminous tracers have been used extensively to map the large-scale matter distribution in the Universe. Similarly the dynamics of stars or galaxies can be used to estimate masses of galaxies and clusters of galaxies. However, assumptions need to be made about the dynamical state or how well galaxies trace the underlying dark matter distribution. The gravitational tidal field affects the paths of photons, leading to observable effects. This phenomenon, gravitational lensing, has become an important tool in cosmology because it probes the mass distribution directly. In these lecture notes we introduce the main relevant quantities and terminology, but the subsequent discussion is mostly limited to weak gravitational lensing, the small coherent distortion of the shapes of distant galaxies by intervening structures. We focus on some of the issues in measuring accurate shapes and review the various applications of weak gravitational lensing, as well as some recent results.

Lecture given as part of the International School of Physics Enrico Fermi "New Horizons for Observational Cosmology", Varenna, July 1-6, 2013, eds. A. Melchiori, A. Cooray, E. Komatsu, to be published by the Italian Society of Physics