Alzheimer's disease (AD) is characterized by the progressive alterations seen in brain images which give rise to the onset of various sets of symptoms. The variability in the dynamics of changes in both brain images and cognitive impairments remains poorly understood. This paper introduces AD Course Map a spatiotemporal atlas of Alzheimer's disease progression. It summarizes the variability in the progression of a series of neuropsychological assessments, the propagation of hypometabolism and cortical thinning across brain regions and the deformation of the shape of the hippocampus. The analysis of these variations highlights strong genetic determinants for the progression, like possible compensatory mechanisms at play during disease progression. AD Course Map also predicts the patient's cognitive decline with a better accuracy than the 56 methods benchmarked in the open challenge TADPOLE. Finally, AD Course Map is used to simulate cohorts of virtual patients developing Alzheimer's disease. AD Course Map offers therefore new tools for exploring the progression of AD and personalizing patients care.