The Explanatory Supplement to the Astronomical Almanac offers explanatory materi al, supplemental information and detailed descriptions of the computational mode ls and algorithms used to produce The Astronomical Almanac, which is an annual p ublication prepared jointly by the US Naval Observatory and Her Majesty's Nautic al Almanac Office in the UK. Like The Astronomical Almanac, The Explanatory Supp lement provides detailed coverage of modern positional astronomy. Chapters are d evoted to the celestial and terrestrial reference frames, orbital ephemerides, p recession, nutation, Earth rotation, and coordinate transformations. These topic s have undergone substantial revisions since the last edition was published. Ast ronomical positions are intertwined with timescales and relativity in The Astron omical Almanac, so related chapters are provided in The Explanatory Supplement. The Astronomical Almanac also includes information on lunar and solar eclipses, physical ephemerides of solar system bodies, and calendars, so The Explanatory S upplement expounds upon each of these topics as well. The book is written at a t echnical, but non-expert level. As such, it provides an important reference for a full range of users including astronomers, engineers, navigators, surveyors, s pace scientists, and educators.