Tishrei is the seventh month of the Hebrew calendar.
First day of Tishrei is Rosh Hashana, the start of the Hebrew new year.
Yes, the Hebrew new year starts in the seventh month of the calendar. This is confusing. Go figure.
Tenth day of Tishrei is Yom Kippur, the Day of Atonement.
Nisan is the seventh month after Tishrei, but only in a leap year, when a 30-day thirteenth month (an extra Adar, named Adar 1) is added to the calendar.
Tishrei, Cheshvan, Kislev [Chanukah], Tevet, Shevat, Adar, Adar 1, Nisan.
A leap year occurs about four times during a 13-year cycle.