The Explanatory Supplement to the Astronomical Almanac offers explanatory material, supplemental information and detailed descriptions of the computational models and algorithms used to produce The Astronomical Almanac, which is an annual publication prepared jointly by the US Naval Observatory and Her Majesty's Nautical Almanac Office in the UK. Like The Astronomical Almanac, The Explanatory Supplement provides detailed coverage of modern positional astronomy. Chapters are devoted to the celestial and terrestrial reference frames, orbital ephemerides, precession, nutation, Earth rotation, and coordinate transformations. These topics have undergone substantial revisions since the last edition was published. Astronomical positions are intertwined with timescales and relativity in The Astronomical 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 Supplement expounds upon each of these topics as well. The book is written at a technical, but non-expert level. As such, it provides an important reference for a full range of users including astronomers, engineers, navigators, surveyors, space scientists, and educators.