Natural Disaster Management (NDM, e.g., for wildfires, floods) can be greatly improved by automating precise semantic 3D mapping and disaster evolution prediction to achieve NDM goals in near-real-time. To this end, many heterogeneous extreme data sources must be analyzed and fused: smart drone and in-situ sensors, remote sensing data, topographical data, meteorological data/predictions and geosocial media data (text, image and videos). The lecture focus is on the extreme nature of the data, due to their varying resolution and quality, very large volume and update rate, different spatiotemporal resolutions and acquisition frequencies, real-time needs and multilingualism. Extreme data analytics can help developing an integrated, ground-breaking NDM platform, focusing on real-time semantic extraction from multiple heterogeneous data modalities and sources, on-the-fly construction of a meaningful semantically annotated 3D disaster area map, prediction of disaster evolution and improved communication between service providers and end-users, through automated process triggering and response recommendations. Semantic analysis computations will be distributed across the edge-to-cloud continuum, in a federated manner, to minimize latency. Extreme data analytics will be performed in a trustworthy and transparent way, by greatly advancing state-of-the-art AI and XAI approaches. The constantly updated 3D map and the disaster evolution predictions will form the basis for an advanced, interactive, Extended Reality (XR) interface, where the current situation will be visualized and different response strategies will be dynamically evaluated through simulation by NDM personnel. An innovative, scalable and efficient implementation platform will provide precise NDM support, based on extreme data analytics.