To add to Luison, "already" means "sooner than expected". "not yet" means "not so far", "not until now" e.g. Q. When will you visit Bratislava? A. I have already visited it! I went last year. Q. Have you visited Bratislava yet? A. No, I haven't visited it yet, but I am planning to go next year.

" I have done it yet" is incorrect. We only use "yet" in the negative form as in " I haven't done it yet". Sometimes we can use it in the affirmative as in " we have yet to win a game" which means " we haven't won yet" . " have yet to" is formal English. It is used in formal situations, and is much less common in casual spoken English. Here are some examples of sentences with have yet to: I have written to your company several times in regard to this matter and I have yet to receive a reply.