That the universe contains a disproportionate amount of matter compared to antimatter cannot be explained by the standard model of particle physics; this is because it contains too little charge-parity (CP) symmetry violation. Low energy experiments with atoms and molecules can be extremely sensitive probes for many types of new physics. An active area of research is the search for electric dipole moments (EDMs) of fundamental particles or nuclei; a nonzero EDM would be evidence for new sources of CP violation. Ytterbium monofluoride (YbF) molecules in a supersonic beam are currently being used to measure the electric dipole moment of the electron (eEDM). This thesis presents progress towards a new, more sensitive eEDM experiment that will use a slower YbF beam source and transverse laser cooling to collimate this beam. We have demonstrated laser cooling of YbF in one transverse dimension to less than
100 μK, which is below the Doppler cooling limit. This was done using a Sisyphus-type mechanism called magnetic field induced laser cooling. We also demonstrate polarisation gradient cooling of YbF. After rebuilding and upgrading much of the experiment, we cooled the beam in both transverse dimensions. By scanning experimental
parameters, we have gained insight into the cooling mechanisms, and the optimum conditions for laser cooling. We placed an upper limit of a few mK on the
transverse temperature of the molecules, although I argue that the true temperature must be very much lower. The number of ultracold molecules was carefully quantified and found to be 2.0(4)x10^5 per pulse. These experiments lay the foundations for an eEDM sensitivity improvement by up to a factor of 100.