Rosh HaShanah
Rosh Hashanah is Hebrew for "head of the year," so this holiday is the festival for the new year. It is alsow the first holy day of the Jewish High Holy Days, which continue from Rosh Hashanah through Yom Kippur, at ten-day expanse.
Yom Kippur
Yom Kippur is the final day of the ten-day period known in Judaism as the High Holy Days. The High Holy Days are not a time of celebration but a very serious time of self-examination and spiritual correction.
Sukkot
This festival occurs in the fall following the High Holy Days and Yom Kippur. Prior to the destruction of the second Holy Temple, Sukkot was a fall pilgrimage festival, drawing Jews from all over to Jerusalem to celebrate and offer thanks for the bounties of nature after the ingathering of their crops, in response to Ha Shem's Commandments. Sukkot, which last for seven days, involves more Mitzvot than any other Jewish Holy Day. The most important of these Mitzvot is to build a sukkah, and outdoor, tempory construct that resembles a hut. The sukkah ritually commerorates the temporary home used by the Hebrew people during their forty-year sojourn in the desert under Ha Shem's protection, following their Exodus from Egypt.
Hoshanah Rabbah
Hoshanah Rabbah is the seventh and last day of Sukkot, which is the day before Shmini Atzeret. It is name for the fact that more hoshanot are sain on this day than all the previous days of the festival. On Hoshanah Rabbah the congregation marches around the synagogue seven times, and this is followed by a custom of the beating of an aravah (willow branch) on the floor five times. The final sealing of judgment that begins with Rosh Hashanah takes place on Hoshanah Rabbah.