The present volume represents a unique blending of two fields only recently recognized as related. On one hand lies the field of Combinatorics with roots (at least immediately traceable via generating functions to Umbral Calculus, the specialty at hand) in the 19th century writings of Boole on operator calculus. Both the foundations and much of the history of the Umbral Calculus are explored in great clarity in [R-K-0 and R-R] which have extensive bibliographies. On the other hand is the field of Hopf Algebras, which is usually traced to the paper of Milnor and Moore [MM] but whose first general exposition is little more than a decade old [S].