This work is produced by HM Nautical Almanac Office to provide navigators and astronomers with simple and efficient methods for calculating the positions of the Sun, Moon, navigational planets and stars to a consistent precision with the aid of a personal computer or programmable calculator. Navigators have been using the tables of co-efficients since 1981 for making sight reductions. The explanation includes an algorithm for determining position at sea without the use of sight reductions tables from observations made with a marine sextant. The software package, NavPac, included with this book, is intended for users who have an IBM PC or compatible. The package contains features additional to the book. For example, there is a programme that calculates distance and course for a rhumb line or great circle track. There are also programs to calculate rise and set times and the altitudes and azimuths of all the bodies. Additional astronomical data files are stored on the disk, which can be read into any personal computer. Astronomers, navigators, surveyors and general users should find these data files useful for making astronomical calculations that require the positions of the Sun, Moon, planets and bright stars.