I. The Mesopotamian traditions
In the sky-map of ancient Babylon, constellations had two different roles, and thus developed into two overlapping traditions. One set of constellations represented the gods and their symbols; the other set represented rustic activities and provided a farming calendar. Many constellations were shared by the two traditions, but in some regions of sky there were alternative divine and rustic figures. These figures developed in stages from ~3200 BC to ~500 BC. Of the divine set, the most important (although the last to be finalised) were the twelve zodiacal signs, plus several associated animals (the serpent, crow, eagle, and fish), which were all transmitted to the classical Greek sky-map that we still use today. Conversely, the rustic constellations of workers and tools and animals were not transmitted to the West. However, a few of them may have survived in Bedouin Arab sky-maps of the first millennium AD.
II. The Mediterranean traditions
The classical map of the sky, with the 48 Greek constellations, was derived from at least two different pre-Greek traditions. One tradition comprised the 12 signs of the zodiac, with several associated animal constellations, all of which developed over ~3200-500 BC in Mesopotamia in a religious or ritual tradition. These were taken over by the Greeks around 500 BC. However the other Babylonian constellations, their farming-calendar tradition, were not adopted. The other tradition was not Mesopotamian; it comprised large constellations which appear to date from ~2800 BC, probably from the Mediterranean region, devised for the navigators of ships. They include huge bears and serpents which marked the celestial pole and equator at that time, and probably the four anonymous giants which we know as Hercules, Ophiuchus, Bootes, and Auriga, as well as some of the large southern ‘marine’ constellations. The origins of some other constellations, including the Perseus tableau and various animals, are unknown; they may have been new creations of the Greeks. The Greeks assembled the classical sky-map from these different sources between 540-370 BC, but many of the familiar legends were only applied to the constellations later.