  The word problem of a finitely generated group is the formal language of
words over the generators which are equal to the identity in the group. If this
language happens to be context-free, then the group is called context-free.
Finitely generated virtually free groups are context-free. In a seminal paper
Muller and Schupp showed the converse: A context-free group is virtually free.
Over the past decades a wide range of other characterizations of context-free
groups have been found. The present notes survey most of these
characterizations. Our aim is to show how the different characterizations of
context-free groups are interconnected. Moreover, we present a self-contained
access to the Muller-Schupp theorem without using Stallings' structure theorem
or a separate accessibility result. We also give an introduction to some
classical results linking groups with formal language theory.
