The goal of polarimetry is to determine not only the linear and circular birefringences, but also the linear and circular dichroisms in an anisotropic optically active material. The measurements of circular effects are, however, exceedingly more difficult than those of linear ones, because the latter generally overwhelm the former. The long period of 170 years had elapsed from the discovery of optical activity by Arago until the high-accuracy universal polarimeter (HAUP) invented by Kobayashi in 1983 enabled one to measure optical activity and linear birefringence simultaneously along any direction in any material. The general HAUP is as an ultimate polarimeter capable of measuring all of the linear and circular effects in an anisotropic optically active material. General HAUP theory indicates that circular dichroism can be obtained exclusively through the accurate measurement of a characteristic angle introduced in the original HAUP method. In this chapter, the original and general HAUP theories are described and some examples from HAUP experiments are presented.