The magneto-optic Kerr effect (MOKE) is the rotation and ellipticity change of polarised light upon reflection from a magnetic material. This thesis outlines the development of a MOKE setup using a modulation technique to fully characterise the polarisation state of visible light. Whereas alternative polarimetry techniques require separate measurements to quantify the Kerr rotation, θK, and the ellipticity angle, εK, the dual photoelastic modulator (PEM) technique used here simultaneously measures both with a single optical path. A full description and analysis of the optical and electronic setup is given. Emphasis is placed on thermal regulation of the entire setup to reduce signal drift, as well as the identification and minimisation of errors in the dual PEM detection system. The typical angular resolution of both MOKE angles is 12μrad, and a long timescale drift of up to 1.2μrad/hour is present. The spatial resolution of MOKE measurements is 4μm, as limited by the reflective objective lens used. This sets the resolution of magnetic domain images which are obtained by scanning the position of focus across the sample surface using piezoelectric transducers. Three magnetic materials are investigated with the developed MOKE setup. Permalloy (Ni80Fe20) deposited on a nickel seed layer has a large permeability and is of interest as a core material in micro-inductors. Persistent domain structures within separated elements of 5μm thick permalloy are imaged using the scanning MOKE setup. This simple domain structure is only observed in high aspect ratio elements (20×300μm2) with large shape-induced uniaxial anisotropy which is useful for future micro-inductor design. Magnetostrictive galfenol (Fe1-xGax) deposited on a piezoelectric 128° X-cut LiNbO3 substrate is investigated for potential incorporation into surface acoustic wave (SAW) devices. A uniaxial magnetic anisotropy in the Kerr and ellipticity angles align with a strain potentially induced by the lattice mismatch between galfenol and LiNbO3. This anisotropy is present in 250nm thick galfenol films. Despite successful imaging of stripe domains in 250nm thick galfenol following AC demagnetisation along the magnetic hard axis, there is no evidence in the MOKE signal of SAWs controlling magnetostriction in the galfenol surface. Finally, single crystals of Mn3Sn, a hexagonal antiferromagnet with a large anomalous Hall effect signal, are aligned and polished for MOKE measurements. Evidence of a longitudinal ellipticity angle up to 0.12mrad, rather than the previously observed Kerr rotation, is presented. Square magnetic hysteresis is measured within 10° of the easy axis in (01-10), and (2-1-10) surface cuts. In both cases, the (0001) direction serves as the hard axis for which there is no measurable field dependence of θK or εK.