N4
にきがつく
To notice (that), To realize (that)
彼は私の気持ちに気がついたのだろうか。
I wonder if he noticed my feelings.
Explanation
「〜に気がつく」 means 'notice' or 'realize'. You had overlooked or forgotten something, and some trigger suddenly makes you aware of it:
1Noticing a change around you: 「財布を落としたことに気がついた」 (I noticed I had dropped my wallet), 「部屋の汚れに気がつく」 (notice the dirt in the room).
2Sensing someone's feelings: 「彼女の悲しみに気がつかなかった」 (I didn't notice her sadness).
After a verb add 「こと」 or 「の」.
Mixed up with
Three 「気」 phrases: 「気がつく」 is to notice (you didn't know, then suddenly did); 「気をつける」 is to be careful (deliberately on guard): 「車に気をつけてください」; 「気になる」 is to be bothered, can't let it go: 「試験の結果が気になる」.
The object takes 「に」, not 「を」: 「×間違いを気がつく」 is wrong.