It is generally understood that the main role of the cerebellum is in movement planning and coordination, but neuroimaging has led to striking findings of its involvement in many aspects of cognitive processing. Mental visualization is such a cognitive process, extensively involved in learning and memory, artistic and inventive creativity, etc. Here, our aim was to conduct a multidimensional study of cerebellar involvement in the non-motor cognitive tasks. First, we used fMRI to investigate whether the cognitive task of visualization from an immediate memory of complex spatial structures (line drawings) engages the cerebellum, and identified a cerebellar network of both strongly activated and suppressed regions. Second, the task-specificity of these regions was examined by comparative analysis with the task of perceptual exploration and memorization of the drawings to be later visualized from memory. BOLD response patterns over the iterations of each task differed significantly; unexpectedly, the suppression grew markedly stronger in visualization. Third, to gain insights in the organization of these regions into cerebellar networks, we determined the directed inter-regional causal influences using Granger Causal Connectivity analysis. Additionally, the causal interactions of the cerebellar networks with a large-scale cortical network, the Default Mode Network (DMN), were studied. Fourth, we investigated rapid cognitive learning in the cerebellum at the level of short-term BOLD response evolution within each region of interest, and at the higher level of network reorganization. Our paradigm of interleaved sequences of iteration between two tasks combined with some innovative analyses were instrumental in addressing these questions. In particular, rapid forms of non-motor learning that strongly drive cerebellar plasticity through mental visualization were uncovered and characterized at both sub-lobular and network levels. Collectively, these findings provide novel and expansive insights into high-order cognitive functions in the cerebellum, and its macroscale functional neuroanatomy. They represent a basis for a framework of rapid cerebellar reorganization driven by non-motor learning, with implications for the enhancement of cognitive abilities such as learning and memory.