  HI intensity mapping (IM) is a novel technique capable of mapping the
large-scale structure of the Universe in three dimensions and delivering
exquisite constraints on cosmology, by using HI as a biased tracer of the dark
matter density field. This is achieved by measuring the intensity of the
redshifted 21cm line over the sky in a range of redshifts without the
requirement to resolve individual galaxies. In this chapter, we investigate the
potential of SKA1 to deliver HI intensity maps over a broad range of
frequencies and a substantial fraction of the sky. By pinning down the baryon
acoustic oscillation and redshift space distortion features in the matter power
spectrum -- thus determining the expansion and growth history of the Universe
-- these surveys can provide powerful tests of dark energy models and
modifications to General Relativity. They can also be used to probe physics on
extremely large scales, where precise measurements of spatial curvature and
primordial non-Gaussianity can be used to test inflation; on small scales, by
measuring the sum of neutrino masses; and at high redshifts where non-standard
evolution models can be probed. We discuss the impact of foregrounds as well as
various instrumental and survey design parameters on the achievable
constraints. In particular we analyse the feasibility of using the SKA1
autocorrelations to probe the large-scale signal.
