  These are extended notes for a series of lectures on Hall algebras given at
the CRM Barcelona in February 2015. The basic idea of the theory of Hall
algebras is that the collection of flags in an exact category encodes an
associative multiplication law. While introduced by Steinitz and Hall for the
category of abelian p-groups, it has since become clear that the original
construction can be applied in much greater generality and admits numerous
useful variations. These notes focus on higher categorical aspects based on the
relation between Hall algebras and Waldhausen's S-construction.
