The idea of dividing time into periods such as years, months, and weeks developed later, but the concept of a calendar really began in the Bronze Age. There is evidence that people then were marking time, trying to manage and predict events by using the natural rhythm of our days.
The Persians certainly showed this desire to have close awareness of the passage of time but the calendar as we know it began with Julius Caesar, the Julian calendar, later to be replaced by the Gregorian calendar we use today.