Composition of Differential Privacy & Privacy Amplification by Subsampling

This chapter is meant to be part of the book ``Differential Privacy for Artificial Intelligence Applications.'' We give an introduction to the most important property of differential privacy -- composition: running multiple independent analyses on the data of a set of people will still be differentially private as long as each of the analyses is private on its own -- as well as the related topic of privacy amplification by subsampling. This chapter introduces the basic concepts and gives proofs of the key results needed to apply these tools in practice.