A set of FORTRAN functions and subroutines has been written to facilitate calculations, using matrix techniques, of the first order properties of ion-optical systems for particle accelerators. These functions and subroutines generate matrices for various magnetic elements used in ion-optical systems and also program various matrix manipulations. A subroutine to calculate the strength of magnetic quadrupoles required to achieve prescribed focal conditions is available. Functions used to calculate the maximum excursion of a particle trajectory from the optic axis in a magnetic element, to calculate the waist of a particle beam if the emittance satisfies certain conditions, and to calculate the location of the focal plane for an arbitrary ion-optical arrangement have been written. Programs can be written, using these functions and subroutines, to calculate the properties of particular ion-optical systems. Illustrative coding shows how such programs are written. (Author).