This book, together with the preceding Principles of Magnetohydrodynamics (to be referred to as Volume [1]), describes the two main applications of plasma physics, laboratory research on thermonuclear fusion energy and plasma-astrophysics of the solar system, stars, accretion disks, 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. In Volume [1], the classical MHD model was developed in great detail without omitting steps in the derivations. This necessitated restriction to ideal dissipationless plasmas, in static equilibrium and with inhomogeneity in one direction. In the present volume on Advanced Magnetohydrodynamics [2], these restrictions are relaxed one by one: introducing stationary background flows, resistivity and reconnection, two-dimensional toroidal geometry, linear and nonlinear computational techniques and transonic flows and shocks. These topics transform the subject into a vital new area with many applications in laboratory, space and astrophysical plasmas.

The two volumes now consist of five parts:

1. I Plasma physics preliminaries (Volume [1], Chapters 1–3),

2. II Basic magnetohydrodynamics (Volume [1], Chapters 4–11),

3. III Flow and dissipation (Volume [2], Chapters 12–15),

4. IV Toroidal plasmas (Volume [2], Chapters 16–18),

5. V Nonlinear dynamics (Volume [2], Chapters 19–21).

Inevitably, with the chosen distinction of topics for Volume [1] (mostly ideal linear phenomena described by self-adjoint linear operators) and topics for Volume [2] (mostly non-ideal, toroidal and nonlinear phenomena), the difference between “basic” and “advanced” levels of magnetohydrodynamics could not be strictly maintained.