Astrometry is undergoing fundamental changes. The celestial reference frame based on bright optical stars is being replaced by the extragalactic reference frame observed at radio wavelengths by Very Long Baseline Interferometry (VLBI); Hipparcos has proven the capabilities of astrometry from space; photographic plates are being replaced by charge coupled devices (CCDs) as the detectors of choice; optical interferometers are replacing transit circles and astrolabes; accuracies of tenths of arcseconds are being replaced by milli- and microarcseconds; the dynamical reference frame is being replaced by a kinematic reference frame; Global Positioning System observations are changing the determinations of Earth Orientation Parameters; and the theory of general relativity is required as the basis of astrometry.

This book is designed to provide the fundamentals for the new astrometry at the milli- and microarcsecond accuracies. The intent is to start from basic principles, without approximations, and develop the fundamentals of astrometry at microarcsecond accuracies. It is based on the general theory of relativity and the concepts introduced by the International Astronomical Union (IAU) in the past decade. The book provides the definitions and applications of the International Celestial Reference System (ICRS) to astronomy and astrometry. It is also designed to provide the philosophy and concepts of astrometry for the future, the principles behind the algorithms, the reasons for astrometry and its relationships with astronomy, geophysics, planetary sciences, astrophysics, cosmology, and celestial mechanics.