This symposium invites scholarly contributions that explore both the foundational and applied aspects of symmetry principles across electromagnetic, acoustic, and elastic wave phenomena. Symmetry principles are pivotal in structuring physical laws, providing deep insights into the invariance and coherence that govern natural systems. A prime example of this is Maxwell's equations, which inherently incorporate Lorentz and gauge symmetries. Although these symmetries were not fully recognized until Einstein's reinterpretation of Lorentz invariance as a spacetime attribute, their elucidation has profoundly transformed modern physics. Similarly, gauge invariance --- representing a redundancy in mathematical formulation rather than a feature of observable physics --- unveils further regularities in field theories. Consistent with the interdisciplinary spirit of the PIERS conference series, this symposium highlights the parallels between electromagnetism, acoustics, and general wave physics. It focuses on how symmetries in governing equations, such as wave invariance under physical transformations, duality, time reversal, or parity operations, impact wave manipulation, metamaterial design, and energy transport. Topics of interest for this symposium include, but are not limited to, symmetry-driven scattering phenomena in photonic and phononic crystals, topological insulators, non-Hermitian open systems, parity-time symmetric systems, and transformation acoustics/optics. Contributions that focus on the exotic properties emerging from symmetry-breaking are also encouraged.