July 9 (17 Tammuz). Fast of Tammuz. The Fast of Tammuz is associated with the breach of the walls of Jerusalem by the Romans in 70 AD and it initiates the three-week period of mourning leading up to the Fast of Av (Tisha b'Av). Prior to the fall of the second temple, the Fast of Tammuz was associated with the fall of the first temple and is referenced in the Book of Zechariah, Zech 8:19, specifically: "And it came to pass, the word of the Lord of Hosts to me, saying, 'Thus said the Lord of Hosts: A fast of the 4th [month]... will become for the House of Judah for happiness and for joy, and for good appointed times; and the truth and the peace they will love.'" Traditionally, the Fast of Tammuz is also associated with Moses' smashing the original two tablets containing the Ten Commandments, when he saw the idolatry of the Hebrews around the golden calf.
July 30 (9 Av). Fast of Av - Tisha b'Av. The Fast of Av is, the anniversary of the destruction of the first and second temples in Jerusalem (586 BCE by the Babylonians, and 70 AD by the Romans, respectively). This date is associated with other crimes against the Jews, such as the expulsion of the Jews from Spain in 1492. In synagogues, the Book of Lamentations is read on Fast of Av. This is a fast day for observant Jews. Traditionally, there no weddings and no B'nai Mitzvah between the Fast of Tammuz (17 Tammuz 5780/July 9, 2020) and the Fast of Av (9 Av/July 30, 2020).