Brain development is a complex process, and disruptions from its normal course may affect the later neurological outcome of an individual. Preterm infants are at higher risk of disability, since a substantial part of brain development happens outside the mother’s womb, making it vulnerable to a range of insults. Understanding the early brain development during the preterm period is of critical importance and magnetic resonance imaging (MRI) allows us to investigate this. Methodologically, this is a challenging task, as classical approaches of studying longitudinal development over this period do not cope with the large changes taking place. This thesis focuses on the development of tools to study the changes in cortical folding, shape of different brain structures and microstructural changes over the preterm period from longitudinal data of extremely preterm-born infants. It describes a tissue segmentation pipeline, optimised on a postmortem fetal dataset, and then focuses on finding longitudinal correspondences between the preterm and termequivalent brain regions and structures in extremely preterm-born infants using MRI. Three novel registration techniques are proposed for longitudinal registration of this challenging data. These are based on matching the spectral components associated with either the cortical surfaces, diffusion tensor images, or both. These allow us to quantify longitudinal changes in different brain regions and structures. We investigated changes in cortical folding of different lobes, microstructural changes and tracts in the white matter, cortical thickness and changes in cortical fractional anisotropy and mean diffusivity. We used cortical surface registration to look at shape differences between controls and extremely preterm-born young adults to gain an insight into the long-term impact of prematurity. This research may contribute to the development of early biomarkers for predicting the neurological outcome of preterm infants and illuminate our understanding of brain development during this crucial period