Rosh HaShanah - The Jewish New Year

Rosh HaShanah is the Jewish new year and day of judgement, in which G-d judges each person individually according to their deeds, and makes a decree for the following year. The holiday is characterized by the special mitzvah of blowing the shofar.

For a variable number of days before Rosh HaShanah among Ashkenazim, and the entire month of Elul among Sephardim, special additional morning prayers are added known as Selichot.

Erev Rosh HaShanah (evening of the first day) - 29 Elul

Rosh HaShanah (ראש השנה‎) - 12 Tishrei

Rosh HaShanah is set aside by the Mishna as the new year for calculating calendar years, shmita and jubilee years, vegetable tithes, and tree-planting (determining the age of a tree).

According to an opinion in Jewish oral tradition, the creation of the world was completed on Rosh HaShanah. The recitation of Tashlikh occurs during the afternoon of the first day. Rosh HaShanah is always observed as a two-day holiday, both inside and outside the boundaries of Israel. The two days are considered together to be a Yom Arichta, a single "long day".

(Adapted from Wikipedia)