In the Mishnah, Rosh Hashanah is one of four Jewish New Years.
The opening passage of Mishnah Rosh Hashanah lists four calendar beginnings, each serving a different legal or religious purpose. Rosh Hashanah, on 1 Tishrei, begins the year for ordinary calendar reckoning, sabbatical and Jubilee cycles, and certain legal documents. It is the New Year most people mean in everyday speech.
The other three are 1 Nisan, the beginning of the religious or ecclesiastical year and the month-numbering system; 1 Elul, associated in the Mishnah with tithing animals; and Tu BiShvat, 15 Shevat, the New Year for trees and fruit-related agricultural rules.
The number four is easy to confuse with later lists of Jewish festivals or with the two-day observance of Rosh Hashanah. The Mishnah’s point is not that Judaism has four competing universal New Year celebrations, but that different dates begin different kinds of years. Rosh Hashanah itself begins in the autumn, even though Tishrei is the seventh month when months are numbered from Nisan.