What is the contribution of Claudius Ptolemy?

Ptolemy developed several mathematical models to describe the motions of the sun, the moon, the planets and the stars. The book that describes these models is called "The Almagest" or "Ptolemy's Almagest". The models all assume:
1. The earth is stationary.
2. All objects travel with uniform speed on a perfectly circular orbit.
However, a model that placed the earth in the centre of the orbits of all other objects would not work because it does not account for various anomalies, including the varying length of seasons, the irregularity of eclipses of the moons and the retrograde motion of the planets. Ptolemy used two mathematical devices to deal with the anomalies: eccentricity (an offset from the centre of a circle) and epicycles - circular orbits whose centre (or eccentric) itself traveled in a uniform circular orbit.

Much of the material in The Almagest was already known to Greek astronomers. Ptolemy's contribution was to consolidate all known results, make large improvements to the models, and to write it all down in a way that became a standard for the way to present the results of scientific enquiry.

His book was the standard text book for astronomers until his models were ultimately improved by Copernicus, Kepler and Newton.

Ptolemy also wrote a treatise on Astrology, based on his deep knowledge of the motions of the heavenly bodies. This work is called The Tetrabiblos.