  This survey purports to be an elementary introduction to compactly presented
groups, which are the analogue of finitely presented groups in the broader
realm of locally compact groups. In particular, compact presentation is
interpreted as a coarse simple connectedness condition on the Cayley graph, and
in particular is a quasi-isometry invariant. In the appendix, an example of a
Lie group, not quasi-isometric to any homogeneous graph, is given; the short
argument relies on results of Trofimov and Pansu, anterior to~1990.
