First things first, let it be clear that I do not speak to this woman regularly (I rarely see her during work hours). I only see her as she is leaving out the door after her shift. The thing is, she often goes out of her way to say goodnight to me when she is leaving. Sometimes I've had my back turned and walking away, and she still made an attempt to get my attention. One time, while working with another female coworker, I was barely visible behind my work. This woman shouted to me (and I think she waved), GOOD NIGHT XXXX, SEE YOU TOMORROW!" The other female coworker gave me a "wth" look as if she was disgusted that she only spoke to me, or she was surprised that she shouted the salutation as she was leaving with other people, who said nothing. She could be just a friendly and polite person, one could say. Ok, there are also moments when we are sort of in close proximity to each other. Say, walking past each other, or standing idly by waiting for something. During these moments, she sometimes stares at her feet, or stares at me. When we crossed paths recently, as I approached her we made eye contact at a distance, and her eyes darted around as a "oh no here he comes" type of deal, then we made eye contact again, smiled,and spoke to each other. There were times in the past where she would stare at me and not say anything. Not creepy stares, but those "look long enough but don't get caught" kind of stares. One time she was off to my side, I glanced over and she was staring dead at me. I smiled and there was a "oh hey, we inadvertently locked eyes while looking around the room, but I totally wasn't staring at you" smile from her. Then there was a time where she just entered the room and stared at me for maybe two or three seconds and didn't say a word. I thought she was staring at my mustache I was attempting to grow. Maybe she was, I don't know. Why would she stare into my eyes though...? This has been going on for about 1 year. I don't really know what to do. She's about mid level on the totem pole, and I am at the very bottom. I don't want to create an uncomfortable situation for the both of us if I make an attempt to become friends. Although this is a very professional workplace, I fear rumors and teasing will start. Also, there are other coworkers here who are married, so I believe friendship++ is not frowned upon. I'd like to maybe just have a conversation with her about something non work related, but I do not have access to her. I only see her when she is leaving. I can't exactly jump in front of her to chat her up at the exit, as my work does not technically allow that. Any advice?