This well-established textbook gives a general but comprehensive introduction to positional astronomy. Originally based on the author's lecture courses at Cambridge University, it is intended primarily for undergraduates, but, due to its comprehensive nature, it is a very useful reference text for research workers in many branches of astronomy and space physics. The author considers the night sky as the celestial sphere and powerfully exploits the methods of spherical geometry. Most problems in which the precise determination of a heavenly body's position in the sky is important are considered in theoretical detail, and the necessary formulae are derived to a precision that is sufficient for all but the most specialist purposes. The present revision has ensured that the terminology and treatment correspond precisely to current astronomical practice. A guiding principle has been to re-establish compatibility with the Astronomical Ephemeris and, to a lesser extent, with the fuller explanations of the Explanatory Supplement to the Astronomical Ephemeris and the American Ephemeris and Nautical Almanac. Fairly frequent comments added to the text indicate the sometimes modified relevance of the subject matter to modern astronomy. A number of additional exercises help to illustrate the new material.