Magnetohydrodynamics (MHD) is a union of fluid mechanics and electromagnetism and describes the macroscopic interaction of electrically conducting fluids and magnetic fields. Since its initial development in the 1930s, MHD has blossomed into a major area of fluid mechanics, with applications ranging from industry to astrophysics. The original development of MHD lay mainly in dynamo theory, which describes how fluid motions within stars and planets can act to generate and sustain a global magnetic field. Later, MHD became popular in the fusion community as the language that could describe the stability of magnetic fields containing plasma. MHD continues to grow and is an area of intensive research. In recent times, the phenomenon of ‘space weather’ has drawn much attention as solar storms that hit the Earth can have a major technological and economic impact. In order to understand the origin of space weather, we need to study the formation and eruption of storms on the Sun. To model the large-scale mechanics of solar storms, we require MHD. In particular, three key areas of MHD are important for the formation of solar storms: MHD stability theory, magnetic topology and magnetic reconnection. These three fields are active areas of research and have each already undergone significant development. Often, these three topics are treated separately. However, for many applications, including the formation and eruption of solar storms in space weather, the three topics are inseparable. The application of these three topics is not only restricted to space weather but is also becoming essential in understanding plasma physics experiments, tokamaks and spheromaks, and many astrophysical applications. The purpose of this school is to focus on the above three areas and present a unified view, revealing how they connect intimately with each other and the role they play in space weather, astrophysical systems and plasma experiments. We shall go beyond the standard theory, as commonly found in textbooks and undergraduate and postgraduate courses. The lectures will describe many recent developments. For MHD stability theory, classical theory will be reviewed and new mathematics required for important extensions of this theory will be developed. Models of plasmas which require physics that goes beyond standard MHD will be discussed. Magnetic topology will be presented from both theoretical and applied standpoints. The modelling of magnetic reconnection, with connections to helicity and turbulence, will be described. Throughout the school, the links between all the above topics will be emphasized and demonstrated. This school would be ideal for PhD students and postdoctoral researchers working in MHD, both in astrophysical and experimental applications. The lectures would give students not only valuable information but an appreciation of how the various disciplines described above, which they may have encountered separately, fit together to give a more accurate picture of the evolution of magnetic fields in electrically conducting fluids and plasmas.