Our Universe is comprised not only of normal matter but also of unknown components: dark matter and dark energy. This Thesis recounts studies of dark matter haloes, using a technique known as weak... Show moreOur Universe is comprised not only of normal matter but also of unknown components: dark matter and dark energy. This Thesis recounts studies of dark matter haloes, using a technique known as weak gravitational lensing, in order to learn more about the nature of these dark components. The haloes analysed are both those surrounding individual galaxies and those encompassing massive galaxy clusters. In order to better study these haloes, new lensing software is developed and existing lensing theory is advanced in the context of this Thesis. As a result, new higher-order signals are detected and lenses are studied in greater detail than ever before. Show less