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Explore cutting-edge developments in metamaterials research through this one-hour lecture that delves into the manipulation of wave phenomena at the nanoscale. Learn how artificial materials engineered at the microscopic level enable unprecedented control over wave propagation, with particular focus on the role of symmetries in establishing unique optical and acoustic properties. Discover the impact of geometrical rotations, tailored perturbations, and broken time reversal symmetry in controlling wave behavior, breaking Lorentz reciprocity, and enabling topological order, dualities, and phase transitions. Examine fundamental physical principles spanning multiple wave platforms and their practical applications in imaging, energy, sensing, computing, and communications technologies.