Human brain white matter undergoes a protracted maturation that continues well into adulthood. Recent advances in diffusion-weighted imaging (DWI) methods allow detailed characterizations of the microstructural architecture of white matter, and they are increasingly utilised to study white matter changes during development and ageing. However, relatively little is known about the late maturational changes in the microstructural architecture of white matter during post- adolescence. Here we report on regional changes in white matter volume and microstructure in young adults undergoing university-level education. As part of the MRi-Share multi-modal brain MRI database, multi-shell, high angular resolution DWI data were acquired in a unique sample of 1,713 university students aged 18 to 26. We assessed the age and sex dependence, as well as hemispheric asymmetry of diffusion metrics derived from diffusion tensor imaging (DTI) and neurite orientation dispersion and density imaging (NODDI), in the white matter regions as defined in the John Hopkins University (JHU) white matter labels atlas. We demonstrate that while regional white matter volume is relatively stable over the age range of our sample, the white matter microstructural properties show clear age-related variations. Globally, it is characterised by a robust increase in neurite density index (NDI), and to a lesser extent, orientation dispersion index (ODI). These changes are accompanied by a decrease in diffusivity. In contrast, there is minimal age-related variation in fractional anisotropy. There are regional variations in these microstructural changes: some tracts, most notably cingulum bundles, show a strong age-related increase in NDI coupled with decreases in radial and mean diffusivity, while others, mainly cortico-spinal projection tracts, primarily show an ODI increase and axial diffusivity decrease. These age-related variations are not different between males and females, but males show higher NDI and ODI and lower diffusivity than females across many tracts. We also report a robust hemispheric asymmetry in both the volume and microstructural properties in many regions. These findings emphasise the complexity of changes in white matter structure occurring in this critical period of late maturation in early adulthood.