The document discusses the multilevel grid data structure. It is based on space tree partitioning and stores cells on separate grids at different levels. It uses simple indexing to identify and navigate between cells. Two major steps were needed to implement real adaptivity: adaptive topology and data projection. Adaptive topology implements refinement strategies to control grid refinement. Data projection preserves and extends data between time steps and across changing grids, using techniques like integrated Legendre projection. Examples demonstrate using the multilevel grid structure to model problems like moving heat sources and wave fronts.