Born in Rhain in Germany, Bayer was a lawyer by profession. In 1603 he published Uranometria, the most complete catalog of pretelescopic astronomy. To Tycho Brahe's catalog of 1602, he added nearly a thousand new stars and twelve new southern constellations. The catalog's main importance, however, rests on Bayer's innovation of naming stars by letters of the Greek alphabet. Before Bayer, prominent stars were given proper names, mainly Arabic ones such as Altair and Rigel. If not individually named, they would be referred to by their position in the constellation. Bayer introduced the scheme, which is still used, of referring to the brightest star of a constellation by ‘alpha’, the second brightest by ‘beta’, and so on. Thus, Altair, which is the brightest star in the constellation Aquila, is systematically named Alpha Aquilae. If there were more stars than letters of the Greek alphabet, the dimmer ones could be denoted by letters of the Roman alphabet and, if necessary, numbers.

Bayer's other proposed innovation – to name constellations after characters in the Bible – was less successful.