  This exposition article arose from two talks given during the Oberwolfach
Arbeitsgemeinschaft on Totally Disconnected Groups in October 2014.
  This is an introduction to the structure theory of totally disconnected
locally compact groups initiated by Willis in 1994. The two main tools in this
theory are the scale function and tidy subgroups, for which we present several
properties and examples.
  As an illustration of this theory, we give a proof of the fact that the set
of periodic elements in a totally disconnected locally compact group is always
closed, and that such a group cannot have ergodic automorphisms as soon as it
is non-compact.
