The main topic of this thesis is the design and analysis of the Cosmic ORigins Explorer (CORE) telescope, a proposed mission for the ESA M5 mission call. Its focus was the study of the Cosmic Microwave Background (CMB), particularly its polarisation. An ambitious space mission, it would endeavour to detect elusive primordial B-modes. B-modes are considered the key piece of evidence for inflation theory and require extraordinary sensitivity to detect. CORE would house up to 2100 detectors on its large, super-cooled focal plane; granting the high sensitivity and wide field of view (FOV) required for CMB study but leads to challenging optical design. Maynooth’s role was to examine telescope designs capable of delivering diffraction-limited quality field of view over this 50 cm focal plane area. Two telescope designs (Offset Gregorian and Offset Dragonian) were analysed. The import and export of the mirrors with correct surface definition and orientation form a central part of this work. Physical optics analysis program GRASP was used to simulate beams on the sky from various focal plane positions to verify the positioning of different frequency detectors over the focal plane. This work would form a part of the CORE proposal. In addition, analysis was carried out on the receiver of the Large Latin American Millimetre Array (LLAMA) telescope, currently under construction in Argentina. Based on existing Atacama Large Millimetre/submillimetre Array (ALMA) telescope designs, LLAMA is an independent instrument that will be able to study a large array of astronomical phenomenon at millimetre wavelengths. Eventually it plans to form the first South American Very Long Baseline Interferometer (VLBI) array alongside ALMA and the Atacama Pathfinder Experiment (APEX). The Department of Experimental Physics was asked to perform analysis using three frequency bands on the Nasmyth B receiver of the telescope and the author was given the task.