I do not wish to confuse your personal life.. this is only what I think from my perspective.
The decision is entirely yours.
Although you are still feeling emotionally attached to him, it may be best to let him go and you might be able to breathe better without him (as crazy as it sounds).
Him doing these things behind your back means he is probably not fulfilled with his current life (maybe he does not realize the treasures he has, maybe he wants something else).
Maybe he wants to live detached, and by leaving, you can only free him. Maybe he needs to experience hooking up with the whole world to realize some things in life. It is up to him. You have no obligation to accept that behavior - he may later realize it was a mistake, but you do not have to wait for him..
The way I see it, even if you stay with him, you will still be feeling the same way and you will be unable to trust him again, which is the foundation of any strong relationship.
It is maybe best to leave him and have a chance at meeting someone who will be grateful to be with you every day, so much that he would not feel interested in other women (even the most passionate man, when in love, prefers to go to bed with the woman he loves).
A man that cheats, may not necessarily be "bad" as a person, but it does not excuse their behavior. If he is great in general but this broke all your trust, before leaving, you could lay the cards on the table, explain how you felt but also ask him to answer honestly about why he cheated.... Was there a problem that he could have told you about before it gets to cheating?
Maybe he was afraid to tell you something so he resorted to sleeping with other women behind your back (not that smart, I know). Even if he has some logical reason, you still don't have to feel pressured to accept this... this is so that you can understand exactly what happened better.
Even if you divorce, do it on a clean slate, say it all, hear it all.
It will help you have closure and move on.
*If he happens to be the aggressive type, forget what I said, write a long explanatory letter (optional) and move out by surprise. Let the lawyers handle the rest.
