NONTECHNICAL SUMMARY Magnetic materials are central to technologies such as data storage, sensors, and emerging computing devices. Most of these technologies rely on the electrons' magnetic moment, which is like a tiny compass needle carried by electrons, to manipulate and store information. This project explores an exciting new frontier in magnetism, where instead of using simple compass-like moments, it focuses on more complex shapes of magnetism known as "multipole moments", which arise in materials where magnetic moment directions vary in intricate patterns across tiny atomic distances. These complex magnetic structures, especially those found in a class of materials called antiferromagnets, can generate new and useful material responses to electric currents or light, opening the door to entirely new types of electronic devices and sensors. The project will develop theoretical tools to understand how these magnetic shapes behave, how they can be controlled by electric currents or light, and how they can enable novel information processing methods that go beyond traditional electron-magnetism-based electronics (also known as spintronics). Educational efforts alongside the research include mentoring students at various levels, organizing a summer school on symmetry in magnetism, and creating accessible teaching materials that blend modern theory and hands-on computation. Together, these efforts aim to expand both the scientific knowledge and the workforce needed for