The next major step in Big Bang cosmology will be the detection of primordial B-modes in the polarisation pattern of the Cosmic Microwave Background (CMB). These primordial B-modes are extremely faint and unprecedented levels of sensitivity will be required to detect them. The QUBIC (Q & U Bolometric Interferometer for Cosmology) instrument, first proposed in 2008 and now on the verge of being commissioned, aims to detect them by using the novel technique of bolometric interferometry to combine the control of systematics provided by an interferometer and the sensitivity provided by an imager. QUBIC is a ground-based instrument that will be installed in Salta Province, Argentina. This thesis describes the detailed optical analysis of the QUBIC instrument and, in particular, its quasi-optical beam combiner. Two variations of QUBIC are analysed: the full instrument (FI) and a technological demonstrator (TD). It was decided to develop the smaller optical combiner of the TD in 2015. The justification for and analysis of the TD are also presented. The QUBIC FI will observe over two bands: 150 GHz (with a 25% bandwidth) and 220 GHz (with an 18% bandwidth). The operation of the QUBIC optical combiner across these bands was investigated using the techniques of physical optics and electromagnetic mode-matching for the feedhorns. This modelling also provided an insight into multimoded operation of QUBIC in the higher band, which will be useful for future instruments that aim to exploit the phenomenon. The optical modelling in this thesis has been used in the calibration and testing phases of the instrument and will be also useful in the future when observations begin in Argentina.