
die Abwesenheit
absence
The state of not being present or not being there at a particular place.
Während seiner Abwesenheit hat ihn sein Kollege vertreten.
During his absence, his colleague filled in for him.
absence
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absence
The state of not being present or not being there at a particular place.
Während seiner Abwesenheit hat ihn sein Kollege vertreten.
During his absence, his colleague filled in for him.

absence
The lack or nonexistence of something.
Die Abwesenheit von Beweisen bedeutet nicht automatisch, dass er unschuldig ist.
The absence of evidence does not automatically mean that he is innocent.

absent-mindedness
A state of mental distraction or inattention in which a person is not mentally focused on what is happening.
Er starrte mit einem Ausdruck völliger Abwesenheit aus dem Fenster.
He stared out the window with an expression of complete absent-mindedness.
'Die Abwesenheit' (absence) is the noun form of the adjective 'abwesend' (absent/not there). The ending '-heit' is often used to form a noun from an adjective that describes a state.
Der Lehrer war letzte Woche abwesend.
The teacher was absent last week.
If you want to say who is not present, you usually use the genitive or a possessive pronoun. A very common phrase is 'während [jemandes] Abwesenheit' (during [someone's] absence).
Während der Abwesenheit des Chefs wurden keine Entscheidungen getroffen.
During the boss's absence, no decisions were made.
In the meaning 'das Fehlen von etwas' (the lack of something), the preposition 'von' + dative is often used to say what is not present. Alternatively, the genitive can also be used.
Die Abwesenheit von klaren Regeln führte zu Chaos.
The absence of clear rules led to chaos.
You can recognize the meaning 'geistige Zerstreutheit' (mental distraction/absent-mindedness) because it refers to a person's mental state, not their physical presence. It is often intensified by adjectives such as 'geistig' (mental) or 'völlig' (complete).
Sie hörte nicht zu und war in einem Zustand geistiger Abwesenheit.
She wasn't listening and was in a state of mental absent-mindedness.
to be absent / to be missing
When referring to things, fehlen directly indicates that something necessary is not present. Die Abwesenheit names this state as a noun and requires a suitable noun construction. With specific missing things, fehlen usually sounds more natural and simpler.

Die Abwesenheit wichtiger Angaben zu den Kosten macht den Bericht unklar.
The absence of important information about the costs makes the report unclear.
Im Bericht fehlen wichtige Angaben zu den Kosten.
Important information about the costs is missing from the report.