  Combinatorial enumeration leads to counting generating functions presenting a
wide variety of analytic types. Properties of generating functions at
singularities encode valuable information regarding asymptotic counting and
limit probability distributions present in large random structures.
``Singularity analysis'' reviewed here provides constructive estimates that are
applicable in several areas of combinatorics. It constitutes a complex-analytic
Tauberian procedure by which combinatorial constructions and
asymptotic--probabilistic laws can be systematically related.
