To know or become aware of a fact or information; to be informed of or discover something.
新しい法律が来月から施行されることを知った。
I learned that the new law will come into effect next month.
その結果を先に知っていれば、もっと準備できたのに。
If I had known the results earlier, I could have prepared more.
彼が会社を辞めた理由を知りたい。
I want to know why he quit the company.
To sense, feel, notice, or realize something (becoming aware through perception).
部屋に入った瞬間、変な匂いがするのに気づいた。何か燃えているのかなと知った。
The moment I entered the room I noticed a strange smell; I realized something might be burning.
彼女の態度の変化に誰もが気づいたが、本人だけは知らなかった。
Everyone noticed the change in her attitude, but she herself didn't realize it.
To understand or comprehend something — grasp its meaning, reason, or essence.
彼の説明を聞いて、ようやくやり方が知れた。
After hearing his explanation, I finally understood how to do it.
長年の研究で、この現象のメカニズムを知ることができた。
After years of research, we were able to understand the mechanism of this phenomenon.
To remember or be familiar/acquainted with someone or something.
昔の同僚の名前をまだ知っている。
I still remember the name of my former colleague.
彼女はその歌をよく知っているようだ。
She seems to be very familiar with that song.
To experience or go through something (e.g., hardship) and thus know it firsthand.
彼は若いころの苦労をよく知っているから、人の痛みが分かる。
Having experienced hardship in his youth, he understands others' pain.
戦争を知る世代の話は重みがある。
Stories from the generation that experienced war carry weight.
To get acquainted with a person; to come to know someone personally.
パーティーで彼女と知り合った。
I got to know her at the party.
紹介してもらって、たくさんの人を知った。
I was introduced to many people and got to know them.
To have to do with, be concerned with, or be someone's responsibility — often used in negative constructions.
それは私の知るところではない。
That's not something I know about / It's not within my knowledge.
この問題は私の知る範囲外だ。
This issue is outside my area of knowledge / responsibility.