This study investigates abnormalities of grey (GM) and white matter (WM) in Alzheimer's disease (AD), by modeling the AD pathological process as a continuous course between normal aging and fully developed dementia, with amnesic mild cognitive impairment (aMCI) as an intermediate stage. All subjects (9 AD, 16 aMCI patients, and 13 healthy controls) underwent a full neuropsychological assessment and an MRI examination at 3 Tesla, including a volumetric scan and diffusion tensor (DT)-MRI. The volumes were processed to perform a voxel-based morphometric analysis of GM and WM volume, while DT-MRI data were analyzed using tract based spatial statistics, to estimate changes in fractional anisotropy and mean diffusivity data. GM and WM volume and mean diffusivity and fractional anisotropy were compared across the three groups, and their correlation with cognitive functions was investigated. While AD presented a pattern of widespread GM atrophy, tissue loss was more subtle in patients with aMCI. WM atrophy was mainly located in the temporal lobe, but evidence of WM microscopic damage, assessed by DT-MRI, was also observable in the thalamic radiations and in the corpus callosum. Memory and executive functions correlated with either GM volume or fractional anisotropy in fronto-temporal areas. In conclusion, this study shows a comprehensive assessment of the brain tissue damage across AD evolution, providing insights on different pathophysiological mechanisms (GM atrophy, Wallerian degeneration, and brain disconnection) and their possible association with clinical aspects of cognitive decline.