  This text is intended as an introduction to magnetohydrodynamics in
astrophysics, emphasizing a fast path to the elements essential for physical
understanding. It assumes experience with concepts from fluid mechanics: the
fluid equation of motion and the Lagrangian and Eulerian descriptions of fluid
flow. In addition, the basics of vector calculus and elementary special
relativity are needed. Not much knowledge of electromagnetic theory is
required. In fact, since MHD is much closer in spirit to fluid mechanics than
to electromagnetism, an important part of the learning curve is to overcome
intuitions based on the vacuum electrodynamics of one's high school days. The
first chapter (only 39 pp) is meant as a practical introduction including
exercises. This is the `essential' part. The exercises are important as
illustrations of the points made in the text (especially the less intuitive
ones). Almost all are mathematically unchallenging. The supplement in chapter 2
contains further explanations, more specialized topics and connections to the
occasional topic somewhat outside MHD. The emphasis is on physical
understanding by the visualization of MHD processes, as opposed to more formal
approaches.
