  Particle methods play an important role in the study of a wide variety of
astrophysical fluid dynamics problems. The different methods currently in use
are all variants of the so-called Smoothed Particle Hydrodynamics (SPH) scheme
introduced by Lucy and Gingold & Monaghan more than twenty years ago. This
paper presents a complete introduction to SPH in its modern form, and discusses
some of the main numerical properties of the scheme. In particular, the
convergence properties of SPH are studied, as a function of the number of
particles N and the number of interacting neighbors N_n, using a simple
analysis based on sound waves. It is shown that consistency of SPH (i.e.,
convergence towards a physical solution) requires both N -> infinity and N_n ->
infinity, with the smoothing length h -> 0, i.e., N_n/N -> 0.
