The Almagest set out to do something no earlier surviving Greek text had managed: give a single mathematical model that could predict, in advance and with real accuracy, where the sun, moon, planets and stars would appear on a given night. Ptolemy built it on a geocentric foundation, the Earth motionless at the center, the heavens turning around it on nested spheres, but the achievement was not the cosmology, which he inherited, so much as the mathematics laid over it: a system of epicycles, deferents and the off-center equant point that let the model match centuries of prior observational records far better than earlier competing schemes.
The thirteen books move from foundational assumptions about the Earth's shape and position, through solar and lunar theory, to the harder problem of the five visible planets, and close with a substantial star catalog recording the positions and relative brightness of over a thousand stars organized into constellations. That catalog, whatever its own debated originality relative to the earlier work of Hipparchus, became a reference tool used and revised for over a thousand years.
Ptolemy titled the work more modestly, as a mathematical composition; the name Almagest descends from its Arabic title, al-majisti, itself derived from a Greek superlative meaning "the greatest," a name that stuck through Arabic and then Latin transmission and effectively replaced Ptolemy's own.