On the occasion ofthe second edition ofthe book, it appeared necessary to up date information that was already seven years old. Astrometry has recorded tremendous advances during these last years, so that, in addition to cor recting identified errors and misprints, there are many major modifications. Among the events that forced me to modify significantly the contents of the book, the most important are the release of the Hipparcos and Tycho cata logues, the introduction of CCD astrometry, the decision of the International Astronomical Union to adopt a new celestial reference frame, the dramatic improvement of accurate time and frequency standards, the decision taken by space agencies to prepare several new space astrometry satellites and the development of optical interferometry. The description and the consequences of these events have been included in this edition. One of them is that a mi crosecond of arc or microarcsecond (uas) has become a widely used unit. On the contrary, the result was also that the importance of some in struments such as astrolabes or transit circles has decreased. However, I left but because their description unchanged, not only for their historical interest, newer techniques often use similar data reduction methods so that one can refer to them. Conversely, some methods or instruments have evolved and new information is included. Finally, many new references were added to the original list.