This thesis investigates the suitability of BH molecules for laser cooling and describes
progress towards the laser cooling of this molecule. We produce a molecular
beam of BH and measure the branching ratios for the excited electronic state,
A^{1}\Pi(v_{0}=0), to decay to the various vibrational states of the ground electronic state,
X^{1}\Sigma. We verify that the branching ratio for the spin-forbidden transition to an intermediate
triplet state is inconsequentially small. We measure the frequency of the
lowest rotational transition of the X state, and the hyper fine structure in the relevant
levels of both the X and A states, and determine the nuclear electric quadrupole and
magnetic dipole coupling constants. We use a semiclassical model of the molecule-light
interaction to investigate the expected cycling behaviour on the main cooling
transition using light with modulated polarisation. The results of the model are
compared with the effect of modulating the polarisation experimentally using an
electro-optic modulator. In order to repump the population that leaks into the first
vibrationally excited state, we have designed, built and tested a suitable repump
laser and have demonstrated that we can drive the repump transition. We have
also designed a Zeeman slower for slowing molecules to low velocity so that they
can be trapped. Our results show that a relatively simple laser cooling scheme can
be used to cool, slow and trap BH molecules.