My ex wants me back?

He's an ex for a reason. and based on his personality and his set of problems ya described, he doesn't need to be in ur life at all. Just keep in mind all of the drama and nonsense ya put up with when ya was with him. then the answer becomes obvious.

What was the reason for breaking up in the first place?

If you want to get back together then you need to re-evaluate your relationship and decide if it is worth saving. If you decide it is then talk to him about whatever problems you had the led to the break up, if he is willing to work through everything then give him another shot. But don't commit to anything or do anything physical until you've talked it all out.

Well, I guess it may still be difficult if he lashes out at you at all. Is he undergoing treatment for bipolar? Any medication to stabilise his mood? In the end, it's just about what you can handle, and what you want. Only get back together if you'd be happy with the way he is, his bad moods and all.

just because he didn't lash out at you then, doesn't mean that he wouldn't later on. there is a reason why you two broke up in the first place, try not to forget that. being in a relationship with someone who suffers from bipolar disorder is very taxing (personal experience) though not impossible, but I stand by previous statement: exs are exs for a reason. but nobody can tell you what to do, you will do what you want to. even people who have gone through the same thing cannot tell you what to do, because they are not you. you should know what's best for you.