In this thesis, we study the Galilean limit of gravity in 2+1 dimensions and give the
necessary ingredients for its quantisation. We study two groups that play fundamental
role in this thesis, the two-fold central extension of the Galilei and Newton-Hooke
groups in 2+1 dimensions and their corresponding Lie algebras. We construct what
we call \Galilean gravity in 2+1 dimensions" as the Chern-Simons theory of the Galilei
group and generalise this construction to include a cosmological constant which, in
the present setting corresponds to the Chern-Simons theory of the Newton-Hooke
group. Finally, we apply the combinatorial quantisation program in detail to the
Galilei group: we give the irreducible, unitary representation of the relevant quantum
double and fully explore Galilean quantum gravity in this setting. We highlight the
associated structures for the Newton-Hooke group and provide an outline for a similar
quantisation. In doing so, we provide the link between Newton-Hooke gravity, and a
deformation of an extension of the Heisenberg algebra that is well-studied
