The calendar system was set by the Sanhedrin President Hillel II in approximately C.E. 359, but the original details are unknown. It is based on the phases of the moon, however it was adjusted to also fit the tropical year by inserting a leap month about every third year. It is therefore known as a Lunisolar calendar. An ordinary year has 12 months, while a leap year has 13.
Every month starts approximately on the day of a new moon.
A Jewish-calendar day starts at sunset rather than at midnight. In the year 2000 we witnessed the start of Jewish year AM 5761.