My ex boyfriend had an affair but never ask me to leave the relationship I left so a month later he wants to apologize and admitted it was a mistake how should I handle this
It bascially comes down to what sort of a person you are and what your expectations for a successful relationship are. Sure, some people would forgive and forget (or try to) but others would keep walking because they believe the saying "once a cheater, always a cheater".
Your BF may have made a mistake but if he respected and loved you and your relationship together, he wouldn't have gone elsewhere and that action tells you in black and white where you stood with him. In other words, he was either with you or he wasn't, and there's no two ways about it.
By all means let him apologize but that doesn't mean you have to take him back.