The Square Kilometre Array (SKA) will be a formidable instrument for the detailed study of neutral hydrogen (HI) in external galaxies and in our own Galaxy and Local Group. The sensitivity of the SKA, its wide receiver bands, and the relative freedom from radio frequency interference at the SKA sites will allow the imaging of substantial number of high-redshift galaxies in HI for the first time. It will also allow imaging of galaxies throughout the Local Volume at resolutions of <100 pc and detailed investigations of galaxy disks and the transition between disks, halos and the intergalactic medium (IGM) in the Milky Way and external galaxies. Together with deep optical and millimetre/sub-mm imaging, this will have a profound effect on our understanding of the formation, growth and subsequent evolution of galaxies in different environments. This paper provides an introductory text to a series of nine science papers describing the impact of the SKA in the field of HI and galaxy evolution. We propose a nested set of surveys with phase 1 of the SKA which will help tackle much of the exciting science described. Longer commensal surveys are discussed, including an ultra-deep survey which should permit the detection of galaxies at z=2, when the Universe was a quarter of its current age. The full SKA will allow more detailed imaging of even more distant galaxies, and allow cosmological and evolutionary parameters to be measured with exquisite precision.
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