  We introduce a category of noncommutative bundles. To establish geometry in
this category we construct suitable noncommutative differential calculi on
these bundles and study their basic properties. Furthermore we define the
notion of a connection with respect to a differential calculus and consider
questions of existence and uniqueness. At the end these constructions are
applied to basic examples of noncommutative bundles over a coquasitriangular
Hopf algebra.
