  This review discusses Smoothed Particle Hydrodynamics (SPH) in the
astrophysical context, with a focus on inviscid gas dynamics. The
particle-based SPH technique allows an intuitive and simple formulation of
hydrodynamics that has excellent conservation properties and can be coupled to
self-gravity easily and highly accurately. The Lagrangian character of SPH
allows it to automatically adjust its resolution to the clumping of matter, a
property that makes the scheme ideal for many applications in astrophysics,
where often a large dynamic range in density is encountered. We discuss the
derivation of the basic SPH equations in their modern formulation, and give an
overview about extensions of SPH developed to treat physics such as radiative
transfer, thermal conduction, relativistic dynamics or magnetic fields. We also
briefly describe some of the most important applications areas of SPH in
astrophysical research. Finally, we provide a critical discussion of the
accuracy of SPH for different hydrodynamical problems, including measurements
of its convergence rate for important classes of problems.
