Calendars have been around since people started marking time. Prehistoric peoples observed the night sky, and recorded the movement of the moon, planets and stars. A bone found near South Africa contains 29 notches that seem to be in reference to a woman marking her menstrual cycle, or someone observing the cycle of the moon (the word "moon" actually comes from "moonth," or period of about 29 days.) This bone is over 35,000 years old.
The study of astronomy actually evolved from the desire to be able to accurately mark long chunks of time, especially as mankind began to farm. It was important to know when to plant seeds and harvest. This may have also led to the first concepts of religion, as the priest or priestess could calculate and predict when certain celestial events would occur, the most notable being eclipses, in addition to other long-term lunar cycles. Structures like Stonehenge in England and Caracol in Mexico are examples of ancient and accurate obervatories that function, among other things, as calendars. These structures are a few to several thousand years old.
17,000 year old lunar calendar at Lascaux?
But who among the greeks?