  This is the extended version of the talk we gave during the
Arbeitsgemeinschaft on totally disconnected locally compact groups, held in
Oberwolfach in October 2014. We give the definition of the Neretin group of
spheromorphisms of the infinite $q$-regular tree, and describe its natural
totally disconnected group topology, which is not the one that usually appears
as the first guess. We also present the proof of simplicity due to Kapoudjian.
We do not make any claims concerning the originality of the presented results.
