  In this thesis, we employ simplicial methods to study actions, principal
bundles, and bibundles of higher groupoids. Roughly, we use Kan fibrations to
model actions of higher groupoids, we use pairs of a Kan fibration and a
special acyclic fibration to model principal bundles of higher groupoids, we
use inner Kan fibrations over the interval to model bibundles of higher
groupoids. In particular, we show that our definitions given by the simplicial
method agree with those given by the categorification approach to actions,
principal bundles, and bibundles of 2-groupoids. In addition, we use the
simplicial technique to prove a theorem on differentiation of higher Lie
groupoids, which shows that the differentiation functor sends a higher Lie
groupoid to a higher Lie algebroid.
