Strictly speaking, it is permissible to make weddings during the Three Weeks (the period from Shiba Asar Be’Tammuz through Tisha B’Ab). According to the ruling of the Shulhan Aruch, it is only during the Nine Days – from Rosh Hodesh Ab through Tisha B’Ab – that weddings are forbidden. The prevalent custom in our community, however, is not to make weddings from Shiba Asar Be’Tammuz through Tisha B’Ab, as this is an inauspicious time for a couple to begin their marriage. Engaged couples should therefore wait until after Tisha B’Ab to get married.
It is permissible, however, to officially announce an engagement during the Three Weeks, including the Nine Days. Strictly speaking, it is permissible to announce an engagement even on Tisha B’Ab day itself (and even to perform Kiddushin, betrothal, which we customarily do at the wedding). Of course, it is not customary to make an engagement on Tisha B’Ab, but it is certainly permissible to get engaged at other times during the Three Weeks, and for the families to get together to celebrate. However, the event should not have music or dancing; even taking the bride or groom into a circle for a dance without music is forbidden during the Three Weeks. This is a period of somber reflection on the tragedy of the Temple’s destruction, and there are people who sit on the floor each day during this period to cry over this calamity. It would thus certainly be inappropriate to dance during the Three Weeks, even without music.
Summary: The accepted custom is not to make weddings during the Three Weeks. It is permissible, however, to announce an engagement during the Three Weeks, and even during the Nine Days, and for the families to meet, but music should not be played and there should be no dancing (even without music) at the celebration.