The original motivation for studying magnetoconvection came from the interplay between magnetic fields and convection that is observed in sunspots. Since then this subject has developed into a fascinating and important topic in its own right. We therefore decided to write a comprehensive monograph that would cover all aspects of magnetoconvection from the viewpoint of applied mathematics, and as a branch of astrophysical (or geophysical) fluid dynamics. Thus we shall emphasize the role of nonlinear dynamics, and focus on idealized model problems rather than on ambitious realistic simulations.

The properties of convection in an electrically conducting fluid with an imposed magnetic field are interesting not only in themselves but also as the richest example of double-diffusive behaviour. Linear theory allows both steady and oscillatory solutions, while theoretical descriptions of nonlinear behaviour demonstrate the power of bifurcation theory, with examples of bifurcation sequences that lead to chaos, as well as of group-theoretic applications to pattern selection. These mathematical results can all be related to carefully constructed numerical experiments.

Although we shall adopt an applied mathematical approach, our discussion is particularly relevant to the behaviour of magnetic fields at the surface of the Sun, which are now being observed in unprecedented detail, both from the ground and from space. Convection also interacts with magnetic fields in the solar interior, as it does in other stars, and is a key component of solar and stellar dynamos.