There are four new year days: On the first of Nissan is the new year for [reckoning the reigns of Jewish] kings and for [establishing the order of] the holidays.  On the first of Elul is the new year for the tithe of animals. R’ Elazar and R’ Shimon say: [It is] on the first of Tishrei.  The first of Tishrei is the new year for [reckoning] the years, for the Sabbatical years, for the Jubilee years, for the planting [of trees], and for the vegetables.  On the first of Shevat is the new year for the tree; according to the words of Beis Shammai. Beis Hillel say: On the fifteenth thereof.

At four junctures [of the year] the world is judged: on Pesach for the grain; on Shavuos for the fruit of the tree; on Rosh Hashanah all who walk the earth pass before Him like young sheep, as it is said: Who fashions all their hearts together, Who understands all their deeds; and on the Festival they are judged for the water.