A girl with a boyfriend...

Well.. Where to start..
I am a 21 years old male from Sweden and just few months ago i started studying in a university.
I started in a school where i knew nobody, but during my 3rd day a nice girl that i had my eyes on talked to during a tram ride, we talked about the regular stuff, how fun our class is etc.. Now I've been going to the college for around 1.5 months and we already hang out with each other all day and go the same way home..

But here is a problem.. She has a boyfriend who she has been with for 3 years.. He is 6 years older then her and a construction worker(with a brain of a 10 year old). She dint tell it to me like someone who likes their boyfriends does.. She "complains" about him pretty often, she actually never told anything positive about him.. Most of her complaints are "My boyfriend does not want to take me out for dinner", "my boyfriend does not take my to play tennis which i want", "my boyfriend uses "snus"(swedish "chewing tobacco") which i hate" etc.. You get the point.. Also she just recently moved to the town where college is while her boyfriend stayed behind in an other town which can only be reached by taking a train which takes around 45 mins..
Also recently i noticed that she has been quite sad in school sometimes.. When her boyfriend calls her responses during the conversation are "uhmmm" "yeah" "ok" etc and she never even smiles when she talks with him on the phone..

Also this girl shows some "signs" for me.. I am the "intelligent-funny" type of a guy and i make her laugh all the time, i mean sometimes she laughs so hard that she has problems stopping, she even laughs at my stupid jokes when nobody else does... We also share same personality traits and we both came to Sweden from the same country when were just kids.
Now to the advice.. I can see that she is not really happy with her idiotic boyfriend(i know him and she deserves better). So i started making some small moves.. For example our class were supposed to start 12.30 AM so i proposed to her to come to school earlier to "study" for anatomy test, she gladly responded and we basically chatted around for 2.5 hours. I could go on and on, but i would like to know what i should do next..
I mean i dont wont to go too "aggressively" because that might put her in a strange position.. For example i wont go up to her and ask her out for a date at the moment.
Should i continue building on her "trust" or should i do something else?

Again, i know that going for girls with boyfriends is not morally "right".. But i am in love and i cant stop thinking about her even for a minute.

well i think your doing a good job so far :) as for her boyfriend just keep being there for her and showing you care, keep being a good friend, if she is having a rough time with her boyfriend then she will really appreciate it and may eventually realise how good you are too her and break things off with him and pursue a relationship with you, thats my advice for right now anyway

Just some new question...

Bassically its the same atm, we talk in school, we talk on the way home and we often text each other on free time.. I dont want to act to "pushy" so i usually start texting her about how for example her work on some school project is going before i "switch" over to "normal" discussion.. I know some girls like very confident guys, but i know that she currently have a boyfriend and i dont want to act to "pushy" so i not currently texting her "hey, what are you doing on saturday" type of messages..
Is it right thing to do? Or should i go ahead with it.. I know its hard to give good advice over Internet, but i would appreciate some women viewpoints on this.

This is like my story. Flames are burning in the first half of the first year... Lots of new faces, intrigating happenings. After that, they are going to fade.