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We present a detailed overview of the cosmological surveys that will becarried out with Phase 1 of the Square Kilometre Array (SKA1), and the sciencethat they will enable. We highlight three main surveys: a medium-deep continuumweak lensing and low-redshift spectroscopic HI galaxy survey over 5,000 sqdeg;a wide and deep continuum galaxy and HI intensity mapping survey over 20,000sqdeg from z = 0.35 - 3; and a deep, high-redshift HI intensity mapping surveyover 100 sqdeg from z = 3 - 6. Taken together, these surveys will achieve anarray of important scientific goals: measuring the equation of state of darkenergy out to z ~ 3 with percent-level precision measurements of the cosmicexpansion rate; constraining possible deviations from General Relativity oncosmological scales by measuring the growth rate of structure through multipleindependent methods; mapping the structure of the Universe on the largestaccessible scales, thus constraining fundamental properties such as isotropy,homogeneity, and non-Gaussianity; and measuring the HI density and bias out toz = 6. These surveys will also provide highly complementary clustering and weaklensing measurements that have independent systematic uncertainties to those ofoptical surveys like LSST and Euclid, leading to a multitude of synergies thatcan improve constraints significantly beyond what optical or radio surveys canachieve on their own. This document, the 2018 Red Book, provides referencetechnical specifications, cosmological parameter forecasts, and an overview ofrelevant systematic effects for the three key surveys, and will be regularlyupdated by the Cosmology Science Working Group in the run up to start ofoperations and the Key Science Programme of SKA1.

Cosmology with Phase 1 of the Square Kilometre Array; Red Book 2018: Technical specifications and performance forecasts