Sukkot is immediately followed by Shemini Atzeret and Simchat Torah.
In Israel Shemini Atzeret and Simchat Torah are celebrated on the same day.
Outside of Israel Simcḥat Torah is celebrated the day after Shemini Atzeret.
Simchat Torah marks the conclusion of annual Torah Reading and the beginning of a new cycle. This accomplishment is celebrated by taking the Torah scrolls out of the ark, and circling the synagogue with them while dancing and singling.
The circling of the synagogue with the Torah is called Hakafot הקפות
When is Simchact Torah and Shemini Atzeret celebrated, in 2012?
Shemini Atzeret and Simchat Torah are celebrated from October 7, 2012 sunset until the first stars on Oct 8, 2012
Outside of Israel:
Shemini Atzeret is celebrated from October 7, 2012 sunset until the first stars on Oct 8, 2012
Simchat Torah is celebrated from first stars of October 8, 2012 until the first stars on Oct 9, 2012