In this book frequency measurements on fast lithium ions as a test of time dilation are presented. The measurements are carried out at the Max Planck Institute for Nuclear Physics in Heidelberg using the storage ring TSR. The transition frequency of a two-level system in the lithium ion is measured using a Doppler-free fluorescence saturation spectroscopy. The spectroscopy is realized by two counter-propagating lasers that are collinearly aligned with the stored ion beam. Two measurements are carried out, one at a ion velocity of 3% speed of light and one at 6.4% speed of light. The measured...