This book describes the two main applications of plasma physics, laboratory research on thermonuclear fusion energy and plasma-astrophysics of the solar system, stars, accretion discs, etc., from the single viewpoint of magnetohydrodynamics (MHD). This provides effective methods and insights for the interpretation of plasma phenomena on virtually all scales, ranging from the laboratory to the Universe. The key issue is understanding the complexities of plasma dynamics in extended magnetic structures.

The book starts with an exposition of the elements of plasma physics, followed by an in-depth derivation of the MHD model. By means of the conservation laws, different model problems for laboratory and astrophysical plasmas are formulated. The spectral theory of MHD waves and instabilities is then developed in analogy with quantum mechanics. The centrepiece is the analysis of inhomogeneous plasmas with intricate spectral structures that provide a unified view of waves and instabilities in plasmas as different as tokamaks and coronal flux tubes. This is illustrated by the magnetic structures and dynamics observed in the solar system, and analysed in detail for cylindrical flux tubes. Advanced chapters on wave damping and resonant heating expose the wonderful interplay of physics and mathematics.

In order to provide the student with all the tools that are necessary to understand plasma dynamics, the classical MHD model is developed in great detail without omitting steps in the derivations. The necessary restriction to ideal dissipationless plasmas, in static equilibrium and with inhomogeneity in one direction, is more than compensated by the insight gained in the intricacies of magnetized plasmas. With this objective the size of the original manuscript, including advanced topics of magnetohydrodynamics, became impractical so that we decided to split it into two volumes.