MHD waves and oscillations are ubiquitously observed in solar magnetic waveguides in features as small as e.g. the magnetic bright point, as dynamic as e.g. spicules or as large as the Sun’s size itself (see e.g. the dynamo wave). Most of the detected waves are linear and the MHD operator, as predicted by H. Alfven in the 1940s seems to be a very accurate description.

In the first part of the talk, I will introduce the eigenmodes of the linear MHD operator, discuss their properties and embark on how to identify these eigenmodes observationally given the superb cohort of satellite (e.g. SOHO, TRACE, STEREO, Hinode, SDO and IRIS) and ground-based (e.g. DST/ROSA, IBIS, CoMP, SST/CRISP) observations. Next, I will discuss how complete is our mathematical modelling in slab and cylindrdrical geometry, in terms of explaining what is observed. In particular, we will discuss whether the observations can indeed prove that our mathematical modelling is complete.