A remarkable time of human promise has been ushered in by the convergence of the ever-expanding availability of big data, the soaring speed and stretch of cloud computing platforms, and the advancement of increasingly sophisticated machine learning algorithms. Innovations in AI are already leaving a mark on government by improving the provision of essential social goods and services from healthcare, education, and transportation to food supply, energy, and environmental management. These bounties are likely just the start. The prospect that progress in AI will help government to confront some of its most urgent challenges is exciting, but legitimate worries abound. As with any new and rapidly evolving technology, a steep learning curve means that mistakes and miscalculations will be made and that both unanticipated and harmful impacts will occur. This guide, written for department and delivery leads in the UK public sector and adopted by the British Government in its publication, 'Using AI in the Public Sector,' identifies the potential harms caused by AI systems and proposes concrete, operationalisable measures to counteract them. It stresses that public sector organisations can anticipate and prevent these potential harms by stewarding a culture of responsible innovation and by putting in place governance processes that support the design and implementation of ethical, fair, and safe AI systems. It also highlights the need for algorithmically supported outcomes to be interpretable by their users and made understandable to decision subjects in clear, non-technical, and accessible ways. Finally, it builds out a vision of human-centred and context-sensitive implementation that gives a central role to communication, evidence-based reasoning, situational awareness, and moral justifiability.