Short answers, pulled from the story.
Claudius Ptolemaeus was a Roman citizen living in Alexandria, Egypt, during the second century of the Common Era. He was born sometime between 100 and 170 AD and died in Alexandria, the only city where his death is concretely evidenced.
The Almagest is the only surviving comprehensive ancient treatise on astronomy, originally titled the Mathēmatikē Syntaxis. It is controversial because modern scrutiny suggests Ptolemy manipulated observational data to fit his geometric models, a claim highlighted by astronomer Robert R. Newton in 1977.
Ptolemy mapped the inhabited world by providing a catalogue of 8,000 localities with assigned coordinates to place them in a grid spanning 180 degrees of longitude. He measured latitude from the equator and expressed it as climata, the length of the longest day, rather than using degrees of arc.
The Tetrabiblos is an astrological treatise in four parts that served as the astrological counterpart to the Almagest. It was first translated from Arabic into Latin by Plato of Tivoli in 1138 while he was in Spain.
Ptolemy wrote the Harmonics, a work on music theory that introduced the harmonic canon or monochord to measure relative pitches. He also wrote the Optica, which survives in a poor Latin version and discusses properties of sight including reflection, refraction, and binocular vision.
Ptolemy believed that mathematics was the only way to secure certain knowledge and was superior to theology or metaphysics. He argued that humans should use both reason and sense perception to arrive at the truth, a view that informed his scientific method.