Rosh HaShanah (the Festival of Trumpets/the Jewish New Year) begins at sundown, October 3 and goes through sundown October 4, 2016. This is the first day of the Jewish year 5777.
Yom Kippur (the Day of Atonement) begins at sundown, October 12, 2016.
Sukkot (Tabernacles) begins at sundown, October 17, 2016 and goes through October 23.
Hanukkah (Festival of Lights) begins at sundown on December 25, 20156. Light candles for 8 nights.
Purim (from the Book of Esther) begins at sundown March 12, 2017.
Passover begins at sundown April 10, 2017 and goes through April 17.
Shavuot (Weeks/Pentecost) begins at sundown May 31, 2017 and goes through June 1.
Tisha B’Av (Destruction of Temple) begins at sundown August 1, 2017.
For those who are interested in knowing more about the Jewish calendar an excellent website is linked here: jewfaq.org/calendar