The motivation for this work is two-fold: the application of general relativity to the metrology of time on one hand (part II), and the use of the methods and technology of time metrology for tests of relativity on the other (part I). In Part I detailed theory for the treatment of the metrology of time in a relativistic context is developed. It provides mathematical expressions for application to the syntonisation and synchronisation of clocks and the realisation of the time coordinates of space-time reference systems. The theoretical expressions are developed to accuracies exceeding those of previous publications in order to accommodate any development in clock and time-transfer technology that can be expected in the near f uture. Part III presents two original experiments which test the theory of special relativity using state-of-the-art time metrology. The first experiment uses data from clock comparisons betweeng round clocks and clocks on board the Global Positioning System( GPS) satellites to test the second postulate of special relativity (the universality of the speed of fight). The experiment is sensitive to a possible anisotropy of the one-way speed of flight in any spatial direction, and on a non-laboratory scale (baselines; -> 20000 Ian) and provides the most stringent limits for the anisotropy published up to date. The second is a proposal for a test of special relativity using a spacecraft that carries an onboard atomic clock and uses a two way time transfer system. The potential accuracy of such a test is evaluated for the ESA/RSA ExTRAS (Experiment on Timing Ranging and Atmospheric Sounding)experiment which was planned for launch in 1997 but is now "on hold".