This depends entirely on what forgiveness entails. If by forgiving her you're thinking that you should take her back then you're going to need to seriously consider what your needs are in a relationship. It's difficult enough to forgive a cheater, but to take one back and maintain a decent relationship with her is even harder. So here are a few questions you should ask yourself before forgiving a cheater.
Are you ok with open relationships?
This is something seriously worth considering. Technically, it's only cheating when there is no arrangement concerning monogamy. It's monogamy itself that created the phenomenon of adultery, cheating, and infidelity. If you are ok with being in a relationship that is emotionally monogamous but sexually, you can do as you please. There are a lot of people out there who prefer this kind of arrangement because sexual exclusivity simply does not suit their personalities or desires well. If you're in a situation with your girlfriend where she seems to genuinely want to be in a relationship with you and you can handle the fact that she is sleeping with other guys, while you also have the option of sleeping with other girls then you have a very good shot of not only forgiving her infidelity, but saving the relationship too.
Why did she cheat?
Nine times out of ten, women who are pretty much done with their current relationship begin “emotionally cheating” on you with the next guy they want to be with. They begin forming a connection with him while their connection with you becomes weaker and weaker. They have all kinds of ways of communicating this with you without really coming out and saying it. In this instance there is no way to save your relationship, nor would you really want to if your head was in the right place. Guys form emotional connections with women and then for whatever reason, the more attached they become, the less the woman seems to want to be with them. While lots of silly reasons exist as to why this happens frequently, the fact is that this phenomenon is purely situational. In cases where becoming overly attached to the girl does push her away, it's not because all women are predisposed to be pushed away by attachment, but rather because she never wanted your relationship to progress to that kind of attachment in the first place, and once it did, she backed off and found someone else .
Should you forgive a cheater?
Yes. Ask yourself this. If she had been honest about her intentions to dump you and start seeing another guy would you have magically felt better about that? Probably not. So even if she broke up with you first it wouldn't have been emotionally any better on you. The question of how to forgive a cheater is probably weighing on you a bit, so the thing you want to ask yourself is how is hanging on to all this resentment benefitting you? It isn't. In fact not only is it hurting you, but it's preventing you from moving on and establishing a new relationship with someone else. Chances are she'll get bored with next guy too and continue to jump from one relationship to the next. No matter how much you cared about her you need to let her go. Don't dwell on her, and do whatever you have to do to avoid thinking about her.