Any system for fixing the beginning, length, order, and subdivisions of the year. Calendrical systems have been used by societies since the earliest times, nearly all of them based on one of two astronomical cycles: the cycle of the phases of the Moon (the synodic month or lunation), often of major ritual and religious significance, and the cycle of the seasons (the period of the Earth's orbit around the Sun), of importance in agriculture. The two cycles are incompatible in that the synodic month has a period of about 29.5 days, giving a lunar year (12 months) of just over 354 days, over 11 days shorter than the mean solar year of 365.2422 days.
The Julian calendar was introduced to the Roman Empire by Julius Caesar in 46 bc. It was developed from the traditional Roman lunar calendar, as is evident from its division into 12 months. However, the months no longer corresponded to lunations, as days were added to give a total year length of 365 days. Almost exact correspondence with the mean solar year was maintained by the intercalation of a leap year containing an extra day, on 29 February, every four years. The average length of the year was therefore 365.25 days which is only slightly longer than the length of the mean solar year. The Gregorian calendar, first introduced in 1582 by Pope Gregory XIII and in almost universal civil use today, superseded, with only slight modification, the Julian calendar. The Gregorian reform of 1582 omitted ten days from the calendar that year, the day after 4 October becoming 15 October. This restored the vernal equinox to 21 March and, to maintain this, three leap years are now suppressed every 400 years, centurial years ceasing to be leap years unless they are divisible by 400. The average length of the calendar year is now reduced to 365.2425 days, so close to the mean solar year that no adjustment will be required before ad 5000.
Other calendrical systems continue to be used, particularly for religious purposes, alongside the Gregorian system. The present Jewish calendar uses the 19-year Metonic cycle made up of 12 common years and 7 leap years. The common years have 12 months, each of 29 or 30 days, while the leap years have an additional month. The rules governing the detailed construction of the calendar are very complicated but the year begins on the first day of Tishri, an autumn month. Years are reckoned from the era of creation (anno mundi) for which the epoch adopted is 7 October 3761 bc. The Islamic calendar is wholly lunar, the year always containing 12 months without intercalation. This means that the Muslim New Year occurs seasonally about 11 days earlier each year. The months have alternately 30 and 29 days and are fixed in length, except for the twelfth month (Dulheggia) which has one intercalatory day in 11 years out of a cycle of 30 calendar years.