The study of the large-scale structure of the Universe is one of the most important tools used to understand the origin and evolution of the Universe. In this thesis, we focus on two different facets of this study: cosmological perturbation theory and cosmic shear. par Cosmological perturbation theory describes how the large-scale structure of the Universe has been created out of the tiny initial perturbations. This evolution is described using fluid equations, and in this thesis, we introduce new versions of this Boltzmann hierarchy. The advantages and disadvantages of each hierarchy are thoroughly analysed. We also introduce a novel technique, dubbed the eikonal approximation, which enables us to better understand the results of existing perturbation theory approaches. Moreover, its broad range of applicability allows us to generalise many results. par Cosmic shear describes how gravitational lensing deforms the image of the sky. In this thesis, we compute in great detail the bispectrum of cosmic shear to second order in the gravitational potentials. The complete calculation is done on the full sky, making the results much more general than the existing ones. To ease the otherwise impossible numerical calculations, we introduce the (extended) Limber approximation.

IPhT