This book considers the ways in which the concept of the Rule of Law will need to evolve in order to ensure that the exercise of power by Artificial Intelligence (AI) does not become arbitrary and does not proceed unchecked. It presents the Rule of Law and its impact on the past and the present; it considers what AI is, what it does, and what it might become in future; and it looks at how AI will need to be harnessed to allow power to be exercised more effectively in the future. The book argues that the Rule of Law has for centuries been the concept that protects against the arbitrary exercise of power. However, the exercise of power by AI unchecked by humans strains the concept's ability to provide this protection.