  Lie groups over local fields furnish prime examples of totally disconnected,
locally compact groups. We discuss the scale, tidy subgroups and further
subgroups (like contraction subgroups) for analytic endomorphisms of such
groups.
  The text is both a research article and a worked out set of lecture notes for
a mini-course held June 27-July 1, 2016 at the MATRIX research center in
Creswick (Australia) as part of the "Winter of Disconnectedness". The text can
be read in parallel to the earlier lecture notes arXiv:0804.2234 which are
devoted to automorphisms, with sketches of proof. Complementary aspects are
emphasized.
