IRA is a Fortran library that solves the shape matching problem for atomic structures, stored as sets of points representing the atomic positions. In the case of exact-and near-congruence, IRA provides the optimal rigid transformation between the structures, given by the atomic assignments, the rotation/reflection matrix, and the translation vector. IRA is also able to operate on structures containing a non-equal number of atoms, i.e. matching a structure to any of its fragments. Any application that requires the solution of a shape matching problem could benefit from IRA.