  The following is an amalgamation of four preprints and some computer programs
which together represent the current state of our investigations of higher
order links. This investigation was motivated by questions discussed and raised
in the first author's paper "New States of Matter Suggested by New Topological
Structures". An important motivation has been to suggest the synthesis of new
types of molecules (see the relevant articles listed in the bibliography). This
discussion is not final, but we think that the results and methods are worth
making public and would be useful for other investigators.
