Ha! This one is interesting, it means "to think about, to talk about" but works as a preposition. That's what I don't get; it's the same with the word (prep) "considering".
"Considering that she likes me, I decided to hit on her".
"Given that you don't like me, I decided to not hit on you".
"Given the truth that you don't like me, I..."
Kind of like "regarding" (providing etc), which could be either a gerund or a perposition.
Regarding the topic, I ain't got nothing to say.
Literally you could deem the word "given" like how a so-called "non-finite" verb works:
(Being) given the situation, I choose to be clever.
Sort of like: I'm given the situation, thus I think... or, now that you give me the situation, I'm supposed to...
Just like: (Being) cheated by her, I decide to cheat her too.