  Quantum affine bundles are quantum principal bundles with affine quantum
structure groups. A general theory of quantum affine bundles is presented. In
particular, a detailed analysis of differential calculi over these bundles is
performed, including the description of a natural differential calculus over
the structure affine quantum group. A particular attention is given to the
study of the specific properties of quantum affine connections and several
purely quantum phenomena appearing in the context of quantum affine bundles.
Various interesting constructions are presented. In particular, the main ideas
are illustrated within the example of the quantum Hopf fibration.
