Last Shabbat of the Year
This is the date when G-d began His creation of the world we live in. (Adam was created on the sixth day which we celebrate as Rosh Hashanah.)
On the night following this last Shabbat of the year it is customary in Ashkenazic synagogues to initiate the Selichot prayers which carry on until Yom Kippur.
What is the connection between the last Shabbat of the year, the date of Creation and the beginning of Selichot?
The security of the world and the Jewish people in particular depends on the Selichot forgiveness we seek for our mistakes of the year coming to an end. And what better way to start the process of teshuva return to G-d than properly observing the last Shabbat of the year as an investment in the peace and prosperity of Israel forever.