Automorphisms of the Baumslag-Gersten group

We classify homomorphisms of the Baumslag-Gersten group into itself. We prove it is Hopfian and co-Hopfian. We show that the group of outer automorphisms of the Baumslag-Gersten group is isomorphic to the dyadic rationals with the addition operation. These results are not new. They were obtained by Andrew M. Brunner in \cite{Brunner}. However, our exposition is self-contained and, hopefully, more accessible for some readers.