What is the religious ruling concerning a husband who swore to divorce his wife by saying, "I call upon Allah to bear witness that you are divorced from me, if you leave the house without my permission, or without my knowledge," and then his wife left without his knowledge?

A conditional divorce intended to take effect upon the fulfillment of the condition is an enforceable divorce. So, if you intended to make your wife’s divorce conditional on her going out without your knowledge, and she did indeed go out, then the divorce has occurred. If this was the first or second divorce, you can take her back before her waiting period (iddah) ends. However, if it was the third divorce, she has become irrevocably separated from you (baynunah kubra), and she is not permissible for you unless she marries another husband willingly, and he divorces her or dies, and her waiting period ends.