The Bayer designation is convention to name stars introduced by Johann Bayer in his work, Uranometria, published in 1609. It consists in a Greek letter, followed by the genitive form of the name of the constellations (exemples: Alpha Aurigae, Beta Orionis, etc.). The system is often abbreviated by writing the corresponding Greek letter in lower cap with the three letters abbreviation of the constellation (exemples: α UMi, η Car)
The system was used as a way to have uniformous names for the stars of the constellations. Even though the brightest star of a constellation is very often referred to as Alpha, the system was by no mean a way to classify the stars by their apparent magnitude, as at the time, there was no way to precisely measure the magnitudes.