(Serious) Should I approach her or not?

There's this girl I really like in my work place and I've been seeing her for a month and I haven't talked to her yet.

I really like her and I don't know her name or age. Either she's my age 23 or slightly 2 years older. Not sure she's a permanent employee.

I made some observations on her.
1. She is very very introverted and not a people person.
2. She stares at me when I'm far away and ignores me when I'm near.
3. She looks at me when I'm not looking at her
4. She searches for me casually when entering cafeteria (Where we often come)
5. She tries to sit in a place where I can't see her face or have eye contact.
6. She looks at me very angrily when eye contact happens.(she won't even blink and feels like death stare)

Should I approach her or she staring at me angrily is a way of telling me not to approach her? Or should I approach her as a friend?
(Serious) Should I approach her or not?
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