
damals
back then
Refers to a specific point in time or period in the past, usually one that was quite some time ago.
Ich war damals 20 Jahre alt und studierte in Berlin.
I was 20 years old back then and was studying in Berlin.
back then
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back then
Refers to a specific point in time or period in the past, usually one that was quite some time ago.
Ich war damals 20 Jahre alt und studierte in Berlin.
I was 20 years old back then and was studying in Berlin.
'Damals' is made up of 'da' (there/then) and 'mals'. 'Mals' is an old form of 'Mal' (point in time/occasion). So the word literally means 'at that point in time' or 'at that time'.
Damals gab es noch keine Smartphones.
Back then, there were no smartphones yet.
As an adverb, 'damals' (back then) can appear in different places in the sentence. If it is in position 1, the verb follows directly after it. But it can also stand after the verb and the subject.
Damals wohnten wir noch in einem kleinen Dorf.
Back then, we still lived in a small village.
'Damals' is often used when telling stories from the past. It refers to a point in time that is already known to the listener or has been established in the conversation, and it creates a narrative atmosphere.
Erinnerst du dich an unseren Urlaub in Italien? Damals waren die Kinder noch ganz klein.
Do you remember our vacation in Italy? Back then, the children were still very little.
there / since / then
Da and damals can refer to a point in the past. Da tends to refer more specifically to a particular moment, while damals explicitly highlights a past period or a longer stretch of time. Use da for the event and damals for the earlier phase of life or situation.

Damals wohnte ich noch mit meiner Schwester zusammen.
Back then, I was still living with my sister.
Da bekam ich plötzlich einen Anruf von meiner Schwester.
Then I suddenly got a call from my sister.