The ability to produce mirrors for large astronomical telescopes is limited by the accuracy of the systems used to test the surfaces of such mirrors. Typically the mirror surfaces are measured by comparing their actual shapes to a precision master, which may be created using combinations of mirrors, lenses, and holograms. The work presented here develops several optical testing techniques that do not rely on a large or expensive precision, master reference surface. In a sense these techniques provide absolute optical testing.The Giant Magellan Telescope (GMT) has been designed with a 350 m2 collecting area provided by a 25 m diameter primary mirror made out from seven circular independent mirror segments. These segments create an equivalent f/0.7 paraboloidal primary mirror consisting of a central segment and six outer segments. Each of the outer segments is 8.4 m in diameter and has an off-axis aspheric shape departing 14.5 mm from the best-fitting sphere. Much of the work in this dissertation is motivated by the need to measure the surfaces or such large mirrors accurately, without relying on a large or expensive precision reference surface.One method for absolute testing describing in this dissertation uses multiple measurements relative to a reference surface that is located in different positions with respect to the test surface of interest. The test measurements are performed with an algorithm that is based on the maximum likelihood (ML) method. Some methodologies for measuring large flat surfaces in the 2 m diameter range and for measuring the GMT primary mirror segments were specifically developed. For example, the optical figure of a 1.6-m flat mirror was determined to 2 nm rms accuracy using multiple 1-meter sub-aperture measurements. The optical figure of the reference surface used in the 1-meter sub-aperture measurements was also determined to the 2 nm level. The optical test methodology for a 1.7-m off axis parabola was evaluated by moving several times the mirror under test in relation to the test system. The result was a separation of errors in the optical test system to those errors from the mirror under test. This method proved to be accurate to 12nm rms.Another absolute measurement technique discussed in this dissertation utilizes the property of a paraboloidal surface of reflecting rays parallel to its optical axis, to its focal point. We have developed a scanning pentaprism technique that exploits this geometry to measure off-axis paraboloidal mirrors such as the GMT segments. This technique was demonstrated on a 1.7 m diameter prototype and proved to have a precision of about 50 nm rms.