  This thesis is based on hep-th/0203110, hep-th/0005273, hep-th/0107068,
hep-th/0106205, and hep-th/0103164, but includes additional results, details,
and background material. It covers the description of D-branes on group
manifolds based on quantum groups including the required mathematical
background, field theory on the q-deformed fuzzy sphere (both first- and
second-quantized), fuzzy instantons, and one-loop results on the fuzzy sphere.
