This course is focused on the problem of enabling analysis of data containing sensitive individual information while preserving the individuals' privacy. The question is motivated by the risks to privacy that come alongside the benefits from sharing and analyzing data. Traditional approaches to privacy, such as anonymizing data by the removal of personally identifiable information have been shown not to provide sufficient privacy, because what seems to be harmless information could serve as an alternative way of identification. We will mostly examine a line of work originated in theoretical computer science that has evolved in the past decade to provide a framework for computing on sensitive datasets -- differential privacy -- in which one can rigorously prove that individual-specific information does not leak in a precise sense. This line of work has established connections to many areas of research including statistics, learning theory, cryptography, computational complexity, convex geometry, mechanism design, databases, programming languages, computer security, statistics, and law and policy.