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In English it is common to reply with "Nice to meet you" when you were introduced to somebody. Likewise you say "Was nice to meet you" on leaving.
Are there any similar phrases a German would use in this context? What is a formal German reply when having been introduced to somebody? Can we say "Es war schön, Sie getroffen zu haben?" when leaving?
coming: "Schön, heute hier sein zu können.", "(Ich bin) Erfreut, Sie kennen zu lernen.", "Ich freue mich auf unsere Zusammenarbeit.", "Guten Tag/Abend", "Angenehm, . (etwas veraltet, sehr höflich)"
leaving: "Vielen Dank für dieses erfolgreiche Treffen.", "Auf Wiedersehen.", "Wir sehen uns morgen."
Meeting, where you have been invited:
coming: "Vielen Dank für die Einladung.", "Vielen Dank für die freundliche Einladung.", "Ihre Einladung hat mich sehr gefreut."
leaving: "Es war schön, Sie kennengelernt zu haben.", "Vielen Dank für den angenehmen/schönen Abend."
official meetings (high society):
coming: "Ich bin sehr erfreut, Sie kennenlernen zu dürfen", "Vielen Dank für die Einladung."
leaving: "Ich habe mich sehr gefreut, Sie kennengelernt zu haben.", "Vielen Dank für diesen angenehmen Abend.", "Es war ein gelungener Abend."
This are some examples of normally used phrases in German to greet someone by coming or leaving. All of this phrases can be changed. For example, you can say "Du" instead of "Sie" if you know the person very well. Or change "Abend" to "Nachmittag" or "Mittag" as needed.
I argue that in German there is no direct translation of "nice to meet you", because German speakers do not express it like that. Clearly, German-dubbed American TV series have already influenced the German language somewhat and some people say that. However being a German native from Bavaria, I find it very artificial to use this expression and believe this is not proper German.
"Sehr erfreut" and similar were in fact common in German in the past (without English influence). However, it sounds very old-fashioned if you are talking to people under 35 and I suggest not using it any more, at least not with younger people (e.g. coworkers at tech companies).
Instead, say something different with a meaning being specific to the situation, e.g.
It is your first day at a new job, you meet your boss or new colleague: At the end of a conversation say "Ich freue mich auf die Zusammenarbeit mit Ihnen." (I am looking forward to working together with you.)
At the end of a pleasant work dinner with your boss or your boss and the wife: "Ich bedanke mich für den schönen Abend." (Thank you for the pleasant evening.)
If you meet a nice man/woman who you hope to see again (formal/work situation): Smile a little and say, "vielleicht begegnen wir uns ja einmal wieder" (maybe we will encounter each again some time) or "bis zum nächsten Mal!" (until next time).
First it depends on whether or not you are actually sincere and acceptable. There is a class system in German. Changing to the personal is established in the course of conversation, time and repeat meetings. If you like to repeat a meeting and things click, you could say: Ich bin sehr erfeut Sie kennenzulernen. If there are repeat meetings and depending on the background of the parties, the Sie can be replaced by the Du or Dich; but that is initiated by the older person. However, it depends in which part of Germany you are. Northerners tends to be more formal and reserved. There are occasions where persons have known each other for a lengthy time, but will remain formal. That is particularly true in working relationships, with neighbors or daily acquaintances.