  Stable surfaces and their log analogues are the type of varieties naturally
occuring as boundary points in moduli spaces. We extend classical results of
Kodaira and Bombieri to this more general setting: if $(X,\Delta)$ is a stable
log surface with reduced boundary (possibly empty) and $I$ is its global index,
then $4I(K_X+\Delta)$ is base-point-free and $8I(K_X+\Delta)$ is very ample.
  These bounds can be improved under further assumptions on the singularities
or invariants, for example, $5(K_X+\Delta)$ is very ample if $(X,\Delta)$ has
semi-canonical singularities.
