
die Vergangenheit
past
The time that has already passed, as opposed to the present and the future.
In der Vergangenheit gab es hier noch keine Hochhäuser.
In the past, there were no high-rises here yet.
past
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past
The time that has already passed, as opposed to the present and the future.
In der Vergangenheit gab es hier noch keine Hochhäuser.
In the past, there were no high-rises here yet.

past
A person's personal life story or background, often with reference to earlier actions or experiences.
Er spricht nicht gern über seine Vergangenheit bei der Armee.
He doesn't like to talk about his past in the army.

past tense
A grammatical tense that expresses that an event took place before the time of speaking.
Im Deutschen gibt es mehrere Zeitformen für die Vergangenheit, zum Beispiel das Perfekt und das Präteritum.
In German, there are several tenses for the past, for example the perfect and the preterite.
'Vergangenheit' (past) is a nominalization derived from the verb 'vergehen' (to pass, to go by). So it literally describes the time that has already 'vergangen' (passed).
Die Zeit vergeht so schnell, wenn man Spaß hat.
Time passes so quickly when you're having fun.
The combination 'in der Vergangenheit' (in the past) is a very common expression for referring to earlier times. It often appears at the beginning of a sentence.
In der Vergangenheit war die Kommunikation ohne Internet viel schwieriger.
In the past, communication without the internet was much more difficult.
When it is about a person's life story, 'Vergangenheit' (past) is often combined with adjectives such as 'schwierig' (difficult), 'bewegt' (eventful), or 'kriminell' (criminal). You can also say 'seine Vergangenheit hinter sich lassen' (to leave one's past behind).
Er hatte eine schwierige Vergangenheit, aber hat sein Leben geändert.
He had a difficult past, but he changed his life.
You can recognize this meaning by the fact that the word is used in a context about language or grammar. Typical signal words are 'Zeitform' (tense), 'Tempus' (tense), 'Perfekt' (perfect), or 'Präteritum' (preterite).
Für das Sprechen über die Vergangenheit benutzt man im Deutschen meist das Perfekt.
To talk about the past, German usually uses the perfect tense.
story / history
Geschichte focuses on past events and how they developed. Vergangenheit refers more to the period or stage of life that has passed. Someone who tells what happened earlier speaks of Geschichte; someone who means an earlier period as a distinct stage speaks of Vergangenheit.

Viele Konflikte des Landes liegen weit in der Vergangenheit.
Many of the country's conflicts lie far in the past.
Das Museum zeigt die wechselvolle Geschichte des Landes.
The museum presents the country's turbulent history.