The principles of the high-accuracy universal polarimeter (HAUP) are discussed. The exact formula is derived for the intensity of the light that traverses the polarizer-sample-analyser system. For measurements with nearly crossed polarizers and oriented close to one of the extinction directions of the samples, the exact HAUP formula can be approximated. The approximate formula is used for the interpretation of the experiments. The fitting procedure that is used to derive the birefringence, optical activity, linear and circular dichroism from the data is described. It takes into account the systematic errors in the equipment due to the ellipticities of the polarizers and the so-called delta-Y-error, which is caused by the eccentricities of the rotation stages that orient the polarizers. The fitting procedures are illustrated with measurements on a sample of (N(CH3)4)2ZnCl4.