There is this girl, and......well...
A year or so ago, we started talking and she showed all the signs of liking me, drawing faces on my papers smiling, trying to start conversations etc. But being the socially terrible and sleep deprived me I am I never took notice, this year I found out she had a "crush" on me and so gave her my number, we went to the movies etc, then I screwed up by making her think I hated her by not being able to talk to her and having a generally soulless default face when I'm zoned out didn't help either.
So she got with another guy, a few weeks later she dumped him for some reason or another a few more things happened blah blah blah and now she is quickly glancing, saying hello to me, talking in a sort of nervous tone etc.
The -blam!- do I do?
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First thought is she's trying to give you another chance but ignore that tidbit. I'd be curious to find out what exactly happened. Have you tried talking to her about it? If so you could find out what not to do and hey, maybe you'd even bond in the moment.