In order to demonstrate optical technology readiness for the Advanced X-ray Astrophysical Facility (AXAF), a Wolter Type I telescope was built. This telescope, called the Technology Mirror Assembly (TMA), was designed to have a system resolution of 0.6 arc second and a tight encircled energy performance specification. In order to meet these goals for encircled energy and resolution, an error budget was established, and specifications applied to each optical parameter. These tolerances are nearly an order of magnitude tighter than those required for HEAO-B, the highly successful forerunner of AXAF, which represents the present state of the art. Such stringent tolerances required a considerable advance in the metrology and polishing process. This paper describes the TMA error budget generation, details the metrology instrumentation and performance levels achieved, and discusses the computer controlled polishing process and equipment used to fabricate these X-ray optics. Finally, we illustrate how polishing progress was measured using a mathematical performance prediction model. Subsequent measurement of TMA focal plane performance shows a resolution of less than 0.5 arc second at X-ray wavelengths, which is in good agreement with these predictions and which represents the highest level of X-ray telescope performance ever achieved.