The Hebrew calendar (הלוח העברי ha'luach ha'ivri), or Jewish calendar, is a lunisolar calendar used today predominantly for Jewish religious observances. It determines the dates for Jewish holidays and the appropriate public reading of Torah portions, yahrzeits (dates to commemorate the death of a relative), and daily Psalm reading, among many ceremonial uses. In Israel, it is an official calendar for civil purposes and provides a time frame for agriculture.
Originally the Hebrew calendar was used by Jews for all daily purposes, but following the conquest of Jerusalem by Pompey in 63 BCE (see also Iudaea province), Jews began additionally following the imperial civil calendar, which was decreed in 45 BCE, for civic matters such as the payment of taxes and dealings with government officials.
The Hebrew calendar has evolved over time. For example, until the Tannaitic period, the months were set by observation of a new crescent moon, with an additional month added every two or three years to keep Passover in the spring, again based on observation of natural events, namely the ripening of the barley crop, the age of the kids lambs and doves, the ripeness of the fruit trees, and the relation to the Tekufah (seasons.) Through the Amoraic period and into the Geonic period, this system was displaced by mathematical rules. The principles and rules appear to have been settled by the time Maimonides compiled the Mishneh Torah in the 12th century.