The Hebrew calendar is a lunisolar system: its months are set by the moon, each beginning near the new moon, while the year is kept in step with the sun by adding a thirteenth month in seven years out of every nineteen. An ordinary year runs twelve lunar months of 353 to 355 days; a leap year, with its added month of Adar, runs 383 to 385. Its era, Anno Mundi, counts from the traditional date of creation, placed at 3761 BCE, so its years run in the fifty-eight hundreds and beyond. The intercalated month holds Passover in the spring as the Torah requires, and the whole is governed by fixed arithmetical rules settled in the early medieval period. These are the features of the Jewish calendar tradition, which orders the festivals and the religious year of Judaism.
The nineteen-year leap cycle follows the Metonic cycle, the same nineteen-solar-year period in which 235 lunar months closely match 235 lunations, independently identified by the Athenian astronomer Meton in the fifth century BCE and adopted into the fixed Hebrew calendar attributed to the Nasi Hillel II around 358 to 359 CE. Years 3, 6, 8, 11, 14, 17 and 19 of the cycle carry the extra month, Adar I, with the regular Adar becoming Adar II in those years. Before Hillel II's fixed arithmetic, the calendar had been set by direct observation, witnesses testifying to the Sanhedrin that they had seen the new crescent moon, supplemented by messengers who carried word of the sighting to Jewish communities outside the Land of Israel; the shift to a calculated calendar removed the need for that observational and communication network. The calendar also applies four dechiyot, postponement rules, that can shift the start of Rosh Hashanah by a day or two to keep certain festivals off inconvenient weekdays.