Preprint.Abstract: We review theory and applications of weak gravitational lensing. After summarisingFriedmann-Lemaitre cosmological models, we present the formalism of gravitational lensing and light propagation in arbitrary space-times. We discuss how weak-lensing effectscan be measured. The formalism is then applied to reconstructions of galaxy-cluster massdistributions, gravitational lensing by large-scale matter distributions, QSO-galaxy correlations induced by weak lensing, lensing of galaxies by galaxies, and weak lensing of the cosmic microwave background.