The Nine Days
What is the purpose of the 9 days and what are we supposed to be doing?
This is the period of the mourning for the destruction of our 2 Holy Temples. The Gemara in Yoma states that the First Holy Temple was destroyed because of the 3 Cardinal sins
gilui arayot (adultery), avodah zora (idol worship) and shichut damin (murder), and the 2nd Holy Temple was destroyed because of sinat chinam ( baseless hatred.)
We need to do a cheshbon hanefesh ( to analyze & account for these reasons the 2 Temples were destroyed), so we can serve Hasehm with avodah shebalev, merit redemption from this long gallus and be zoche to see the rebuilding of the 3rd Temple.