Part I. Astrometry in the Twenty-First Century: 1. Opportunities and challenges for astrometry in the twenty-first century M. Perryman; 2. Astrometric satellites L. Lindegren; 3. Ground-based opportunities for astrometry N. Zacharias; Part II. Relativistic Foundations of Astrometry and Celestial Mechanics: 4. Vectors in astrometry, an introduction L. Lindegren; 5. Relativistic principles of astrometry and celestial mechanics S. Klioner; 6. Celestial mechanics of the N-body problem S. Klioner; 7. Celestial coordinate systems and positions N. Capitaine and M. Stavinschi; 8. Fundamental algorithms for celestial coordinates and positions P. Wallace; Part III. Observing through the Atmosphere: 9. The Earth's atmosphere: refraction, turbulence, delays and limitations to astrometic precision W. van Altena and E. Fomalont; 10. Astrometry with ground-based diffraction-limited imaging A. Ghez; 11. Optical interferometry A. Glindermann; 12. Radio interferometry E. Fomalont; Part VI. From Detected Photons to the Celestial Sphere: 13. Geometrical optics and astrometry D. Schroeder; 14. CCD imaging detectors S. Howell; 15. Using CCDs in the time-delayed integration mode D. Rabinowitz; 16. Statistical astronomy A. Brown; 17. Analyzing poorly-sampled images: HST imaging astrometry J. Anderson; 18. Image deconvolution J. Nuñez; 19. From measures to celestial coordinates Z. H. Tang and W. van Altena; 20. Astrometric catalogs: concepts, history and necessity C. López; 21. Trigonometric parallaxes F. Benedict and B. McArthur; Part V. Applications of Astrometry to Topics in Astrophysics: 22. Galactic structure astrometry R. Méndez; 23. Binary and multiple stars E. Horch; 24. Binaries: HST, Hipparcos and Gaia D. Pourbaix; 25. Star clusters I. Platais; 26. Solar System astrometry F. Mignard; 27. Extrasolar planets A. Sozzetti; 28. Astrometric measurement and cosmology R. Easther; Appendices; Index.