0 to think that something is true, or that what someone says is true -- ~を信じる, (~であると)確信する
She says she’s only 30, but I don’t believe it.
Do you believe him?
1 to think something, although you are not completely sure -- ~だと推測する
2 used to say that something surprising is true -- 信じられないかもしれないが, なんと
He even remembered my birthday, believe it or not.
3 to be very surprised when you see someone or something, or when you hear what someone says -- 目を疑う/ 耳を疑う