Cosmology with the Square Kilometre Array

We review how the Square Kilometre Array (SKA) will address fundamental questions in cosmology, focussing on its use for neutral Hydrogen (HI) surveys. A key enabler of its unique capabilities will be large (but smart) receptors in the form of aperture arrays. We outline the likely contributions of Phase-1 of the SKA (SKA1), Phase-2 SKA (SKA2) and pathfinding activities (SKA0). We emphasise the important role of cross-correlation between SKA HI results and those at other wavebands such as: surveys for objects in the EoR with VISTA and the SKA itself; and huge optical and near-infrared redshift surveys, such as those with HETDEX and Euclid. We note that the SKA will contribute in other ways to cosmology, e.g. through gravitational lensing and $H_{0}$ studies.