  The original Bondi$-$Metzner-Sachs (BMS) group B is the common asymptotic
symmetry group of all asymptotically flat Lorentzian 4-dim space$-$times. As
such, B is the best candidate for the universal symmetry group of General
Relativity (G.R.). Here, the analogue $B(2,1)$ of $B$ in 3 space$-$time
dimensions is properly defined. We study its representation theory in the
Hilbert topology by using an infinite-dimensional extension of Wigner-Mackey
theory. We obtain the necessary data in order to construct the strongly
continuous irreducible unitary representations (IRS) of B(2,1). The main
results of the representation theory are: The IRS are induced from ``little
groups'' which are compact. There is one infinite connected ``little group'',
the special orthogonal group SO(2). There are infinite non$-$connected finite
discrete ``little groups'', the cyclic groups C_{n} of even order. The inducing
construction is exhaustive notwithstanding the fact that B(2,1) is not locally
compact in the employed Hilbert topology. B(2,1) is also derived, in Klein's
sense, as the automorphism group of the ``strong conformal geometry'' of future
null infinity. Besides the Hilbert topology other reasonable topologies are
given to B(2,1) and their physical relevance is discussed. Connections of the
IRS of B(2,1) with geometry are outlined.
