I don't think any of us can say whether you should or shouldn't leave your boyfriend. It's not black and white, there's no 'well they cheated so that's an automatic end of the relationship'. We on TSR don't know you, don't know your boyfriend and don't know your relationship. Only you can make this decision. The things to think about if you want to get back with him are:
1. Do you think you can trust him again?
2. What things would you like him to agree to to help you move on from this and regain your trust in him? This might be, for example, that you don't want him getting drunk on nights out without you, no contact with this other girl, etc.
3. Do you think he would do it again?
4. Can you put it past you? If you can imagine being together in ten years time, say, and get into an argument over something stupid like whose turn is it to empty the bin, if you think you would constantly go 'well you're the one who slept with that girl that one time!' then that's not a healthy relationship to be in.
5. Do you only want to stay with him because you're afraid that if he goes you'll be alone forever? This is the most important one. I know how scary this can hit you, but trust me one day in the future you'll realise that true love won't have passed you by in your teens/twenties! Obviously we all have those dark, insecure moments, but you won't always feel like that. So if your reason for not breaking up with him only comes down to you not wanting to be alone, that is not a good reason to stay.