“Nice to meet you!” means “Рад(а) познакомиться!” (“Rad(a) poznakomitsa!”) or “Приятно познакомиться!” (“Priyatno poznakomitsa!”) in Russian. You can also say “Рад(а) встрече!” (“Rad(a) vstreche!”).
If you want to be especially poilte, you can use these phrases – “Ochen rad(a!)” or “Ochen priyatno!”. But before that you can tell a person your name.
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