About 3 weeks ago me and my girlfriend broke up. The last month of our relationship was just going worse and worse. Sometimes I didn’t even understand why are we arguing mostly it was about me doing something stupid apparently and needing to change. Except I still didn’t know what I had to change. It felt like she was trying to make big thing out of nothing most of the time.

The thing is the last month we been together I started noticing something is wrong. From the way she acted, talked to me etc. So I was trying to make things better, now I know it was a little too much sometimes. And not getting angry, trying to talk about it listening to what she has to say, being nice to her up until we broke up.

After the breakup we didn’t talk for a few days. And then went to a party together, both invited by other people by coincidence basically. Everything was calm. The next day I found out her “friend" was telling her things about me. Bad things which were completely untrue. So she rang me and ended up arguing. I tried talking calmly with her a couple of times but she wouldn’t have any of it and we ended up saying really bad things at each other and her getting angrier and angrier. She told me to just off and don’t talk to her anymore.

A few days ago I found out/realized what I actually have done to make her angry in the first place, so I apologized sincerely and for anything horrible I said to her. Told her I hope she can forgive me. Her reply was "I don’t care".

Even with all the horrible things she said to me I am still in love with her and care for her very much. I know right now I need to give her space for a while and not talk at all. My question is there any way this can be salvaged? I know she still cares deep down but just doesn’t show it. If she was serious she would have deleted me from her life all together, which I know she hasn’t.

Maybe write her one last message about realizing your mistake and offering another apology (only if it is warranted however). Let her know how much you care about her and would like to get things back on track. Acknowledge that the communication will have to improve on both your parts and let her know that you are willing to work towards that. Either she wasn't very clear on what she was upset about, or you weren't really listening to what she was saying, or it was a combination of both.

Then leave it alone. She will know how you feel, what you want, and what you are willing to work on with her. It will then be up to her to make the next move.

If after a period, however long you are comfortable with, you don't get any indication from her that she is receptive to the idea, you let the relationship go and move on.

Either she wasn't very clear on what she was upset about, or you won't really listening to what she was saying, or it was a combination of both.

That's pretty much spot on, a combination of both.

I am definitely willing to work on everything, since we broke up she was my motivation to get my life in order, "grow up" if you will.
I think right now it's a little early to tell her anything, I'm afraid if I tell her all these things about me realising my mistake, she will not listen or just reply with a f off or leave me alone.
She is extremely angry at me at the moment and she can be very stubborn at times. She has some qualities about her personality that can make it very hard for you to make things better, if she doesn't like you.

Then give it some time. Let things settle a bit and see what happens. Maybe she will contact you, maybe not. After awhile you can decide what you want to do next.

In the meantime, do something's that you enjoy. Spend time with friends and family.

That's what I'm hoping will happen, that she will contact me first.

I do get a bit impatient sometimes though and start talking first, I know because I did it a few times before to her, and it didn't end well. That was 1 of my mistakes. Sort of like "the more i did to fix it the more i damaged the relationship".
Also it doesn't help that we work in the same place just different departments so I see her pretty much everyday still. I tried even avoiding the places she works in or goes to but to no avail.

If she hasn't calmed down in 3 weeks and forgiven you, she may never. I know its hard having to see her every day, but its time to avoid her completely, and get your own happiness in order.

Don't be discouraged by how hard that will be, or how long it may take, just stay with it, and do better with somebody else.