
unter
under
Indicates a position that is spatially lower than something else.
Die Katze schläft unter dem Bett.
The cat is sleeping under the bed.
under
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under
Indicates a position that is spatially lower than something else.
Die Katze schläft unter dem Bett.
The cat is sleeping under the bed.

among
Expresses belonging to a group or a position in the midst of something; among, in the midst of.
Unter den Bewerbern war auch ein alter Schulfreund.
Among the applicants was an old school friend.

under
Indicates a condition or circumstance under which something happens.
Unter diesen Umständen können wir nicht weiterarbeiten.
Under these circumstances, we cannot continue working.

under / below
Indicates that a value, number, or age is not reached or exceeded; less than.
Kinder unter sechs Jahren haben freien Eintritt.
Children under six years old get free admission.

under
Describes hierarchical subordination or dependency.
Er arbeitet direkt unter der Geschäftsführung.
He works directly under management.

during
Indicates that something happens during a particular event or state.
Unter der Fahrt wurde ihm schlecht.
He felt sick during the trip.
'Unter' is a two-way preposition. You use the dative for a position (question: 'Wo?' (Where?)) and the accusative for movement in a direction (question: 'Wohin?' (Where to?)).
Der Ball liegt unter dem Tisch. (Wo? → Dativ)
The ball is under the table. (Where? → dative)
In most figurative, non-spatial meanings, 'unter' is used with the dative. This applies, for example, to conditions, groups, or numerical information.
Unter diesen Umständen ist das nicht möglich.
Under these circumstances, that is not possible.
As a verb prefix, 'unter-' can be separable or inseparable. The stress determines this: 'úntergehen' (separable, to sink / go down) has the stress on the prefix, while 'unterschréiben' (inseparable, to sign) has the stress on the verb stem.
Die Sonne geht am Horizont unter.
The sun is setting on the horizon.
In the meaning of 'in the midst of a group', 'unter' is often used in fixed expressions. Examples are 'unter uns gesagt' (between you and me / confidentially) or 'unter Freunden' (among friends).
Das bleibt aber unter uns, ja?
This stays between us, okay?
To express a condition, 'unter' is often used. Typical phrases are 'unter der Bedingung, dass…' (on the condition that…), 'unter diesen Umständen' (under these circumstances), or 'unter keinen Umständen' (under no circumstances).
Unter keinen Umständen darfst du diese Tür öffnen.
Under no circumstances may you open this door.
To express that a number, age, or value is not reached, you use 'unter' with the dative. It then means 'less than'.
Der Eintritt ist für Kinder unter 12 Jahren kostenlos.
Admission is free for children under 12 years old.
from / of
Von selects part of a larger group. Unter, by contrast, places people or things within that group. Drei von zehn Bewerbern therefore emphasizes the selected subset, while unter den zehn Bewerbern presents the same people as members of the group.

Unter den zehn Bewerbern haben drei bereits Berufserfahrung.
Among the ten applicants, three already have professional experience.
Drei von zehn Bewerbern haben bereits Berufserfahrung.
Three out of ten applicants already have professional experience.