Right now I wouldn't take her back since she's been with another man.
Hold onto this. Keep believing it. It could be that she'll work her butt off eventually to win you back, but you can't base your life on the eventuality that she MAY want to try again. Move forward, as you are doing, with the understanding that it's over. Work on yourself. Make this be her loss.
You cannot be lonely if you like the person you're alone with. Dr. Wayne Dyer