Is it permissible for a girl to marry another man without being divorced from the first one, who legally contracted with her by agreement, held a wedding feast, and received the dowry, but did not consummate the marriage or formalize the contract?

Know that merely agreeing, paying the dowry, and holding a feast does not constitute a marriage; rather, it is a form of engagement. Marriage has its conditions and pillars, such as offer and acceptance.

If what occurred was merely an engagement, then the other man's engagement to you and marriage to you before the first engagement was annulled is a reprehensible act for which repentance is due, but it does not affect the validity of the marriage if it was concluded fulfilling its conditions.

However, if what was first concluded was a marriage that fulfilled its pillars and conditions, then the second marriage is invalid, because a married woman is among the impediments to marriage. In this case, the second husband must separate from you immediately, and the first husband is not permitted to have intercourse with you except after performing istibra' from the second.