On the 10th of Tevet in the Hebrew year 3336 (425 BCE), the army of Babylonian emperor Nebuchadnezzar surrounded Jerusalem’s stone walls and laid siege on the city. This was the beginning of the end of the first Beit Hamikdash; on the 17th of Tammuz, 3338, the city walls were breached, and three weeks later, on 9 Av of that year, the Temple was destroyed and the Jews were sent into exile.
The 10th of Tevet is observed as a day of fasting and mourning; the fast begins Tuesday morning and lasts until nightfall.
We wish you an easy fast and may we see the third temple rebuilt in our times.
Source: http://lubavitch.com/news/article/2109183/Today-in-Jewish-History-Asarah-10-B-Tevet.html
