The Hebrew, or Jewish, calendar begins with the month of Nissan and ends with the month of Adar. The calendar is based on the lunar cycle and contains either 12 or 13 months, depending on the year.
The first month, Nissan, generally falls in March or April, and it contains the holy day of Passover. The next months are Lyar, Sivan, Tammuz, Menacham Av and Elul. The seventh month, Tishrei, generally occurs during September or October, and this month contains the holy days of Rosh Hashanah and Yom Kippur. The next month is Marcheshvan. Then come Kislev and Tevet, during which Hanukkah begins and ends, followed by the month of Shevat. The final month is Adar.
The Jewish calendar is based upon a lunar cycle, but it is not a true lunar calendar. A 12-month lunar calendar would be about 11 days short of a solar-based calendar. The Jewish calendar compensates for the discrepancy in a manner similar to the leap year day in the secular calendar. Users of the Jewish calendar add an extra month periodically to keep the months in their proper seasons. The additional month is called Adar I and is inserted prior to the final month of Adar (which is called Adar II in that year).