  A general theory of quantum spinor structures on quantum spaces is presented,
within the conceptual framework of the formalism of quantum principal bundles.
Quantum analogs of all basic objects of the classical theory are constructed
and analyzed. This includes Laplace and Dirac operators, quantum versions of
Clifford and spinor bundles, a Hodge *-operator, appropriate integration
operators, and mutual relations of these objects. We also present a
self-contained formalism of braided Clifford algebras. Quantum phenomena
appearing in the theory are discussed, including a very interesting example of
the Dirac operator associated to a quantum Hopf fibration.
