  This is an extended version of a three part mini course on the Drury-Arveson
space given as part of the Focus Program on Analytic Function Spaces and their
Applications, hosted by the Fields Institute and held remotely. The
Drury-Arveson space, also known as symmetric Fock space, is a natural
generalization of the classical Hardy space on the unit disc to the unit ball
in higher dimensions. It plays a universal role both in operator theory and in
function theory. These notes give an introduction to the Drury-Arveson space.
They are not intended to give a comprehensive overview of the entire subject,
but rather aim to explain some of the contexts in which the Drury-Arveson space
makes an appearance and to showcase the different approaches to this space.
