  In this paper, six constructions of difference families are presented. These
constructions make use of difference sets, almost difference sets and disjoint
difference families, and give new point of views of relationships among these
combinatorial objects. Most of the constructions work for all finite groups.
Though these constructions look simple, they produce many difference families
with new parameters. In addition to the six new constructions, new results
about intersection numbers are also derived.
