Cosmology with Gravitational Lensing

In these lectures I give an overview of gravitational lensing, concentrating on theoretical aspects, including derivations of some of the important results. Topics covered include the determination of surface mass densities of intervening lenses, as well as the statistical analysis of distortions of galaxy images by general inhomogeneities (cosmic shear), both in 2D projection on the sky, and in 3D where source distance information is available. 3D mass reconstruction and the shear ratio test are also considered, and the sensitivity of observables to Dark Energy is used to show how its equation of state may be determined using weak lensing. Finally, the article considers the prospect of testing Einsteins General Relativity with weak lensing, exploiting the differences in growth rates of perturbations in different models.} abstract{In these lectures I give an overview of gravitational lensing, concentrating on theoretical aspects, including derivations of some of the important results. Topics covered include the determination of surface mass densities of intervening lenses, as well as the statistical analysis of distortions of galaxy images by general inhomogeneities (cosmic shear), both in 2D projection on the sky, and in 3D where source distance information is available. 3D mass reconstruction and the shear ratio test are also considered, and the sensitivity of observables to Dark Energy is used to show how its equation of state may be determined using weak lensing. Finally, the article considers the prospect of testing Einsteins General Relativity with weak lensing, exploiting the differences in growth rates of perturbations in different models