The assignment of Greek letters to stars is attributed to Johann Bayer, a German astronomer and cartographer, in his star atlas Uranometria published in 1603.

While Bayer didn't invent the system, he was the first to apply it consistently across the entire sky. He used Greek letters in order of brightness (alpha being the brightest, beta the second brightest, etc.) within each constellation. This system has remained in use for centuries, though it has some limitations and exceptions:

* Brightness: While the brightest star in a constellation is usually designated alpha, there are exceptions where the naming doesn't reflect actual brightness.

* Multiple Stars: Some constellations have multiple stars with the same Greek letter. For example, there are two stars named "alpha Centauri".

* Southern Hemisphere: Bayer's catalog primarily focused on the Northern Hemisphere, so many Southern Hemisphere stars lacked Greek letter designations until later astronomers expanded the system.

Despite these limitations, Bayer's system of Greek letter designations remains a fundamental part of astronomical nomenclature.