  Braided non-commutative differential geometry is studied. In particular we
investigate the theory of (bicovariant) differential calculi in braided abelian
categories. Previous results on crossed modules and Hopf bimodules in braided
categories are used to construct higher order bicovariant differential calculi
over braided Hopf algebras out of first order ones. These graded objects are
shown to be braided differential Hopf algebras with universal bialgebra
properties. The article especially extends Woronowicz's results on
(bicovariant) differential calculi to the braided non-commutative case.
