In this thesis I will study noncommutative differential geometry, after the style of Connes and Woronowicz. In particular two examples of differential calculi on Hopf algebras are considered, and their associated covariant derivatives and Riemannian geometry. These are on the Heisenberg group, and on the finite group A4. I consider bimodule connections after the work of Madore. In the last chapter noncommutative fibrations are considerd, with an application to the Leray spectral sequence. NOTATION. In this thesis equations are numbered as round brackets (), where (a.b) denotes equation b in chapter a, and references are indicated by square brackets []. This thesis has been typeset using Latex, and some figures using the Visio program.