Interpreting someone's actions and intentions can be complex, and it's important not to jump to conclusions without enough information. There could be various reasons why this married woman is looking at you and quickly looking away when you notice her gaze. Here are a few possibilities:
Coincidence: It could be purely coincidental that she's looking in your direction, and her glances might not have any specific meaning or intention.
Attraction: It's possible that she finds you attractive or interesting, and her quick glances are her way of showing subtle interest. However, it's important to remember that even if she is attracted to you, acting on it would not be appropriate, considering she is married.
Curiosity: She might be curious about you for some reason, perhaps because she recognizes you from somewhere, or she finds something about you intriguing.
Unintentional: Sometimes, people might be lost in their thoughts or daydreaming, and their gaze may wander without any intention.
Insecurity: Her quick glances away could indicate that she feels shy or insecure when you catch her looking at you.
Misinterpretation: It's also possible that you are misinterpreting her actions, and her glances may not be directed at you at all.
Regardless of the reason, it's essential to be respectful and not make assumptions or approach her based solely on these glances. If you find her behavior uncomfortable or if you're concerned about the situation, it might be best to avoid engaging with her and respect her boundaries. If the situation persists or becomes problematic, consider discussing it with someone you trust or, if necessary, a professional counselor or therapist for guidance.