  We present a freely downloadable software package for modelling the dynamics
of galaxies, which we call the Torus Mapper (TM). The package is based around
`torus mapping', which is a non-perturbative technique for creating orbital
tori for specified values of the action integrals. Given an orbital torus and a
star's position at a reference time, one can compute its position at any other
time, no matter how remote. One can also compute the velocities with which the
star will pass through any given point and the contribution it will make to the
time-averaged density there. A system of angle-action coordinates for the given
potential can be created by foliating phase space with orbital tori. Such a
foliation is facilitated by the ability of TM to create tori by interpolating
on a grid of tori.
  We summarise the advantages of using TM rather than a standard time-stepper
to create orbits, and give segments of code that illustrate applications of TM
in several contexts, including setting up initial conditions for an N-body
simulation. We examine the precision of the orbital tori created by TM and the
behaviour of the code when orbits become trapped by a resonance.
