[en] The Third IAEA-TM on Theory of Plasma Instabilities provided a forum for open discussion on theoretical and computational physics issues of relevance to burning plasmas. The meeting covered linear and non-linear theory of large and small scale plasma instabilities, including turbulence, magneto-hydrodynamic (MHD) effects and integrated modelling. All physics issues of relevance to the performance of burning plasma devices were covered, but special attention was paid to the modelling and prediction of instabilities generated by fast alpha particles and their role in the plasma confinement. This subject is of significant importance for the ITER project and for the performance of future fusion power plants. The meeting aimed to identify directions for future fusion research in preparation for ITER and fusion power plants