  Smoothed Particle Hydrodynamics (SPH) is a unique numerical method widely
used for astrophysical problems since it involves no spatial grid. Rather,
fluid quantities are carried by a set of Lagrangian `particles' which move with
the flow, meaning that complicated dynamics and asymmetric phenomena are
treated with ease. Since adaptivity is a built-in feature of the method there
is no need to resort to complicated additional mesh refinement procedures. In
this chapter we have undertaken a thorough review of the SPH method in order to
develop a sufficiently accurate method which can be applied to MHD problems
(Chapters 4-5). The review contains several results which have not been
published elsewhere.
