  We demonstrate our recent general results on the Casimir construction and
moduli space of all bicovariant calculi by means of some detailed examples,
including finite-difference and 2-jet cacluli on $\R^n$ and full details of the
Casimir construction of the 4D calculus of $SU_q(2)$. We likewise demonstrate
our previous general constructions with T. Brzezinski of quantum group gauge
theory with examples of such nonuniversal differential calculi on spacetime. We
outline a notion of quantum homotopy of a quantum space. We indicate a possible
application to classical integrable systems.
