What the difference between: "Nice to meet you" and "Nice to meeting you"
I think that you use the first one when you meet someone for the first time, and the second when you already know that person (for a short time) and you say goodbye... Am I right? I´m not sure at all... :)

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The second version is completely incorrect. The first is OK but rather informal. If you want to say something on parting, you can say "It is a pleasure to have met you" or more informally, "It was nice meeting you" , "It has been nice meeting you". A lot depends on the context - is this an informal meeting or an interview for a job for example?

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The expression is "Nice TO MEET you" or "Nice MEETING you." (If you use the -ing, there is no "to.")

Some people feel that the -ing greeting shows more emotion.

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When you first meet somebody, you could say 'It IS nice to meet you' (present tense).
The short form for this sentence is 'nice to meet you'.
After you have met somebody, and you are leaving, you could say 'It WAS nice to meet you' (past tense).
The short form for this sentence is also 'nice to meet you'.