The Solar Wave Theory Group (SWAT), as part of the Solar Physics and Space Plasma Research Centre (SP²RC) at the University of Sheffield, has established a world-leading role in solar and space plasma wave physics by its work on wave processes from the sub-surface solar interior to the solar upper atmosphere (corona) using mathematical modelling and analysis of observational data from satellite-borne and ground-based state-of-the-art instruments. Many of the physical phenomena SWAT studies are of a basic nature and fundamental to general plasma astrophysics. Members of SWAT have been especially active in the physical understanding of wave propagation in the near sub-photosphere; seismology from active regions to global magneto-helioseismology; MHD wave coupling of the solar photosphere to the complex magnetised corona through the chromosphere and transition region (and vice-versa!); diagnostic and dynamic role of MHD waves in inhomogeneous plasmas with applications to solar and magnetosphere waveguides; developing and applying the tools of coronal seismology; and investigating instabilities in MHD shear flows. Find out more about SWAT.