eine Zeitlang
for a while
An indefinite, usually shorter period of time. It describes a certain duration without defining it precisely.
Ich habe eine Zeitlang in Berlin gewohnt.
I lived in Berlin for a while.

while
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for a while
An indefinite, usually shorter period of time. It describes a certain duration without defining it precisely.
Ich habe eine Zeitlang in Berlin gewohnt.
I lived in Berlin for a while.

The word is made up of 'Zeit' (time) and 'lang' (long). So literally it describes a 'long time', but it is used for an indefinite period of time.
Das hat eine ganze Zeitlang gedauert.
That took quite a while.
This noun is used almost exclusively in the form 'eine Zeitlang' (for a while) as an adverbial expression of time. It answers the question 'Wie lange?' (How long?). Other forms are extremely rare.
Er hat eine Zeitlang als Lehrer gearbeitet, bevor er Schriftsteller wurde.
He worked as a teacher for a while before he became a writer.
The expression 'eine Zeitlang' (for a while) can stand at the beginning of the sentence (position 1) or in the middle field. If it stands at the beginning, the verb follows directly after it.
Eine Zeitlang war alles in Ordnung.
For a while, everything was all right.
duration
'die Dauer' and 'eine Zeitlang' both talk about a period of time. 'die Dauer' is a normal noun and means how long something lasts. You often use it when you want to know or state the length more precisely. 'eine Zeitlang' is a fixed expression and means: for a certain, not precisely defined time. It sounds less precise and often more everyday. They can be confused because both point to the length of an event or process. If you are asking about the exact length, 'Dauer' fits. If you only want to say that something happens for a while, 'eine Zeitlang' fits.

Nach der Reise blieb meine Schwester noch eine Zeitlang bei uns.
After the trip, my sister stayed with us for a while longer.
Die genaue Dauer des Kurses steht auf der Webseite.
The exact duration of the course is listed on the website.