On Monday I called her to meet up and she agrees to meet me at the library on Friday. Then today i went to the library and texted her if she is here. I waited for an hour and instantly left, then 10 minutes later she texted me telling me that she forgot and she was sorry. I was pissed and she was wasting my time. So I wonder to myself should i give her a second chance or just move on to the next one?

An hour and then she never showed up? Does she know you waited a whole hour?
She texted to say sorry ten minutes after you left. I would give her another a chance if she's hot enough, only
If she invites you out or to something then yes.
but I would absolute never bring it up again to her. Certainly don't whine or anything to her in anyway, basically acting like you didn't even care or miss her at the library, but....

Other than that, you're too valuable to get blown off like that and come asking for a second date. I'm newbie here, but that's my 2 cents.

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Valhalla, I am coming!

You gotta confirm before hand. If you told her on Monday and didn't check on Thursday then that's on you. She forgot regardless, but you should always confirm that something is on before going. Dont say you waited

She flaked. You gotta deal with it. Don't give her a second chance.

You've got to let her know that she missed out on a great time because you're flipping awesome.

So just ignore her cause she blew it, there are more fish in the sea.

But in the future, don't think a library is an interesting place to meet and talk with a girl. No wonder she flaked on you haha.

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Two words: Carpe Diem