einmal
once
Refers to one single time or one single occasion in the past, present, or future.
Ich habe diese Oper nur einmal gesehen.
I have seen this opera only once.

once
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once
Refers to one single time or one single occasion in the past, present, or future.
Ich habe diese Oper nur einmal gesehen.
I have seen this opera only once.

The word is a combination of 'ein' (one) and 'Mal' (time/occasion). It literally means 'one single time' and can refer to the past or the future.
Ich möchte dieses Restaurant noch einmal besuchen.
I would like to visit this restaurant once more.
The meaning of 'einmal' depends heavily on context. When it describes a number of times, it is often stressed. As a filler word in a request, it is unstressed and often sounds like 'mal'.
Ich war nur einmal in Berlin.
I was in Berlin only once.
In spoken language, 'einmal' (often shortened to 'mal') is used to make a request or prompt sound friendlier and less direct. Here it has no literal meaning.
Schau einmal, was ich gefunden habe!
Look what I found!
The expression 'auf einmal' (all at once/suddenly) is a fixed unit and means 'plötzlich' (suddenly). It often appears at the beginning of a sentence and then causes inversion (verb before subject).
Wir saßen im Garten und auf einmal begann es zu stürmen.
We were sitting in the garden, and all at once it started to storm.
The phrase 'Es war einmal ...' (Once upon a time ...) is the traditional and fixed opening of fairy tales in German. It introduces a story that takes place a long time ago.
Es war einmal ein König, der hatte drei Töchter.
Once upon a time, there was a king who had three daughters.
The combination 'nicht einmal' is used for emphasis and means 'not even'. It expresses that even a minimal expectation was not met.
Er war so müde, er hat nicht einmal zu Abend gegessen.
He was so tired that he didn't even eat dinner.
once / times
'mal' and 'einmal' can both make a request or instruction sound softer in colloquial speech. 'Kannst du mal kommen?' and 'Kannst du einmal kommen?' are similar, but 'mal' often sounds more casual and everyday. 'einmal' can also really mean 'one single time', for example when referring to a number of times. In the fixed expression 'auf einmal', it means 'suddenly'; there you cannot simply say only 'mal'. The risk of confusion is high because 'mal' is often a short form of 'einmal', but it does not work the same way in every meaning.

Ben möchte den neuen Film einmal mit einem Freund sehen.
Ben wants to see the new film once with a friend.
Kannst du mir mal kurz mit der Tasche helfen?
Could you just help me with the bag for a moment?