The book is a detailed reference text to the algorithms and theories used to produce The Astronomical Almanac. It covers the history, significance, sources, methods of computation, and use of the data presented in The Astronomical Almanac. Because The Astronomical Almanac prints primarily positional data, this book goes into great detail on techniques to get astronomical positions. The book, however, is not a basic textbook on spherical, dynamical, or positional astronomy. It supplements such textbooks because it contains detailed explanations and current methods of application.

The first edition of the book appeared in 1961. At that time there were two separate publications of the almanac, so the title included both names in full: Explanatory Supplement to the Astronomical Ephemeris and the American Ephemeris and Nautical Almanac. It was prepared jointly by Her Majesty's Nautical Almanac Office (HMNAO) and the U.S. Nautical Almanac Office and published by Her Majesty's Stationery Office. It was reprinted with amendments in 1972, 1974, and 1977. It was then allowed to go out of print because the International Astronomical Union (IAU) introduced such substantive changes to the underlying algorithms and theory that a major revision to the Explanatory Supplement was needed.

The second edition of the book appeared in 1992 with the title Explanatory Supplement to the Astronomical Almanac. It was edited by Dr. P. K. Seidelmann and published by University Science Books, Inc. It contained contributions from the U.S. Nautical Almanac Office, Her Majesty's Nautical Almanac Office, the Jet Propulsion Laboratory, Bureau des Longitudes, and the Time Service and Astrometry Departments at the U. S. Naval Observatory (USNO).

The third edition, available since mid-2012, is a complete revision of the 1992 book; the title remains the same. Each chapter was updated; several of them completely re-written. Along with subjects covered in the previous two editions, it also contains descriptions of the major advancements in positional astronomy over the last 20 years, including: the ICRS replacing the FK5 system; the new precession and nutation theories; and a new positional paradigm that is no longer tied to the ecliptic and equinox. Although most of the authors are from either the USNO or HMNAO, other subject-matter experts contributed.

The book was edited by S.E. Urban and P.K. Seidelmann and is available from University Science Books, Inc.

A list of known errata is found here.