まだ
still, not yet
まだ + verb / まだ + ていません
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まだ means "still" with a positive verb and "not yet" with a negative:
- まだ雨が降っています, "it's still raining"
- まだ食べていません, "I haven't eaten yet"
For "not yet", Japanese uses the ている form, ていません, because it describes the current state: you're still in the not-having-eaten state. 食べませんでした would be "I didn't eat (at that time)", which closes the door.
The quick answer to もう〜ましたか is いいえ、まだです, "no, not yet".
まだまだ is "still far from it", the modest reply to a compliment on your Japanese.
Examples
昼ご飯はまだ食べていません。
I haven't had lunch yet.
雨はまだ降っています。
It's still raining.
いいえ、まだです。
No, not yet.
父はまだ会社にいます。
My father's still at work.
まだ時間がありますから、大丈夫です。
We've still got time, so it's fine.