What is the ruling regarding the oath I swore upon the Qur'an to my first wife, vowing not to speak again to a girl I used to flirt with, and the oath I swore to my children that I had not met any girl before contracting marriage to her, knowing that I had met her and committed adultery with her?

The oath you swore to your wife has two possibilities:

1. That you swore falsely that you did not return the girl's call. This is a Ghamus oath, one of the major sins, and it necessitates sincere repentance without expiation, according to the more preponderant opinion.

2. That you swore not to return to flirting with the girl, but then you did. This is a binding oath that necessitates breaking it (hanth) and an expiation for an oath after repenting from the sin.

As for the oath you swore to your children, it is a Ghamus oath. We advise you to offer sincere repentance for these sins.