TM (Torus Mapper) produces models for orbits in action-angle coordinates in axisymmetric potentials using torus mapping, a non-perturbative technique for creating orbital tori for specified values of the action integrals. It can compute a star's position at any time given an orbital torus and a star’s position at a reference time, and also provides a way to choose initial conditions for N-body simulations of realistic disc galaxies that start in perfect equilibrium. TM provides some advantages over use of a standard time-stepper to create orbits.