  This thesis introduces the notion of "relative gerbes" for smooth maps of
manifolds, and discusses their differential geometry. The equivalence classes
of relative gerbes are classified by the relative integral cohomology in degree
three. Furthermore, by using the concept of relative gerbes, the
pre-quantization of Lie group-valued moment maps is developed, and its
equivalence with the pre-quantization of infinite-dimensional Hamiltonian loop
group spaces is established.
