Tishri-years is an ancient calendar system used in Israel/Judea, and the Jewish people in Diaspora. It is based on, and is a variation of, the Nisan-years.
Tishri-years is often called the Jewish Civil Calendar, in contrast to Nisan-years, which is often called the Jewish Religious Calendar.
Tishri-years is similar to, and sometimes equivalent to, the Macedonian years practices by the Hellenistic empires (332-30 BC). They are all lunisolar years beginning from Autumn, but could differ by a month.
While the Nisan-years begin the year from the Spring season, around the Vernal Equinox/Spring Equinox (Gregorian March 20/21), the Tishri-years begin the years from the Autumn season, around the Autumn Equinox (Gregorian September 22/23). The New Years Day of the Tishri-years is called Rosh Hashanah ("Head of the Year"); it begins the Fall Feasts of Israel.
Tishri 1, however, is not determined directly by its relationship to the Autumn Equinox. It depends on the determination of Nisan 1, which is the day after the New Moon closest to the Spring Equinox (within fifteen days before or after). Tishri 1 is the first day of the seventh month. Although the month number is always counted from Nisan, in the Tishri-years, the year begins and ends with Tishri 1.
The intercalary month is still the second Adar, initially determined by agricalutral observations in Israel. Although meteorological conditions may cause a few days of delay for each Rosh Codesh ("Head of the Month"), over all the errors will cancel each other, and the calendar system remained accurate.
After the fourth century AD, Hillel II fixed the Jewish Talmudic Calendar by a mathermatical algorithm, in order for Jews all around the world to observe the feasts according to the same calendar. This caused the Jewish calendar to gradually depart from the actual seasons, due to the accumulated errors.
The origin of the Tishri-years tradition can be traced to King David, who was ordained the king of Judah (the two southern tribes) on Tishri 1, 1010 BC, before he was ordained the king of Israel (the ten northern tribes) on Nisan 1, 1002 BC. It seemed that David still used the Nisan-years in chronicling his years, but King Solomon made it a national calendar commemorating his great father. And after the split of the kingdom in 931/930 BC, the northern kingdom Israel continued using Nisan-years, while the southern kingdom Judah used the Tishri-years.
The Jewish people kept on using the Tishri-years system throughout the first (Babylonian) and the second (Roman) Diaspora, till today. They also traced the system back till the time of creation.