Weak Gravitational Lensing

This chapter provides a comprehensive overview of weak gravitational lensing and its current applications in cosmology. We begin by introducing the fundamental concepts of gravitational lensing and derive the key equations for the deflection angle, lensing potential, convergence, and shear. We explore how weak lensing can be used as a cosmological probe, discussing cosmic shear, galaxy-galaxy lensing, and their combination with galaxy clustering in the 3$\times$2pt analysis. The chapter covers the theoretical framework for modeling lensing observables, shear estimation techniques, and major systematic effects such as intrinsic alignments and baryonic feedback. We review the current results of weak lensing cosmology from major surveys and outline prospects for future advancements in the field.