Astrometry encompasses all that is necessary to measure the positions and motions of celestial bodies: observational techniques, instrumentation, processing and analysis of observational data, and reference systems and frames, as well as the resulting astronomical phenomena. It is fundamental to all other fields of astronomy, from the focusing of telescopes to navigation and guidance systems and distance and motion determinations for astrophysics. Starting from basic principles, this work provides the principles of astrometry at milli- and micro-arcsecond accuracies and will be an invaluable reference for graduate students and research astronomers.