  The purpose of this dissertation is to examine the BMS symmetry group, which
arises as the asymptotic symmetry group of four-dimensional asymptotically flat
spacetimes at null infinity, and to uncover its relation to the Carroll group.
Firstly, we illustrate how the BMS group emerges from the analysis of the
asymptotic conditions on the gravitational field. We summarise both the
original metric-based method by Bondi, Metzner, van der Burg and Sachs, and the
geometrical approach by Penrose. Then, we analyse the Carroll Group and, in
particular, its conformal extension which, in the case of a conformal
transformation of N=2 level, is equivalent to the BMS group in four dimensions.
The motivation to study the properties of the groups related to the BMS is that
they may shed light on some open question regarding the BMS group itself, such
as its representation theory, its extension to higher dimensions and its use
for flat holography. We conclude by showing an example on how the Carroll group
arises as the symmetry group of plane gravitational waves.
