  We review the geometrical properties of vacuum spacetimes in (2+1)-gravity
with vanishing cosmological constant. We explain how these spacetimes are
characterised as quotients of their universal cover by holonomies. We explain
how this description can be used to clarify the geometrical interpretation of
the fundamental physical variables of the theory, holonomies and Wilson loops.
In particular, we discuss the role of Wilson loop observables as the generators
of the two fundamental transformations that change the geometry of
(2+1)-spacetimes, grafting and earthquake. We explain how these variables can
be determined from realistic measurements by an observer in the spacetime.
