Shavua Tov. Tomorrow is Asara B'Tevet. The fast begins at 5:21 and ends at 5:23 according to Torah Tidbits. It represents the siege of Nebuchadnezzar, King of Bavel on Jerusalem. It lasted three years and ended with the destruction of the First Temple.
The Tenth of Tevet is also designated as יום קדיש הכללי, where Kaddish is recited for those who perished in the Holocaust and their date of death was not known.
According to tradition, there were three fast days in a row on the 8th, 9th, and 10th. The eighth of Tevet was the anniversary of when the Torah was translated into Greek by seventy-two elders. The Torah was intended to be transmitted in Hebrew only and translated orally.
The ninth of Tevet was the date when both Ezra and Nechemia died. May we see the fulfillment of the prophecy of Zechariah that the fast of the tenth month should turn into a day of celebration.