The AXAF-I High Resolution Mirror Assembly (HRMA) consists of four nested mirror pairs of Wolter Type-I grazing incidence optics. The HRMA assembly and alignment will take place in a vibration-isolated, cleanliness class 100, 18 meter high tower at an Eastman Kodak Company facility in Rochester, NY. Each mirror pair must be aligned such that its image is coma-free, and the four pairs must be aligned such that their images are coincident. In addition, both the HRMA optical axis and focal point must be precisely known with respect to physical references on the HRMA. The alignment of the HRMA mirrors is measured by the HRMA Alignment Test System (HATS), which is an integral part of the tower facility. The HATS is configured as a double-pass, autocollimating Hartmann test where each mirror aperture is scanned to determine the state of alignment. This paper describes the design and operation of the HATS.