
montieren
to assemble
To put something together or assemble it from individual parts, for example a piece of furniture or a machine.
Am Wochenende habe ich endlich das neue Bücherregal montiert.
At the weekend, I finally assembled the new bookshelf.
to assemble / mount / edit
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to assemble
To put something together or assemble it from individual parts, for example a piece of furniture or a machine.
Am Wochenende habe ich endlich das neue Bücherregal montiert.
At the weekend, I finally assembled the new bookshelf.

to mount
To attach or install something in a specific place.
Der Elektriker kommt morgen, um die neuen Lampen an der Decke zu montieren.
The electrician is coming tomorrow to mount the new lamps on the ceiling.

to edit
In film and media production, the cutting and combining of individual film sequences or audio tracks into a finished work.
Der Editor wird das gesamte Rohmaterial sichten und den Film montieren.
The editor will review all the raw footage and edit the film.
Verbs that end in '-ieren' are almost always regular. The past participle is formed without 'ge-' ('montiert'), and the simple past ends in '-ierte' ('montierte').
Er hat gestern den ganzen Tag Möbel montiert.
He spent the whole day assembling furniture yesterday.
In the meaning 'zusammenbauen' (to assemble), 'montieren' is typically used with objects that consist of parts. These include: furniture, a wardrobe/cabinet, a bicycle, or a machine.
Kannst du mir helfen, dieses komplizierte Gerät zu montieren?
Can you help me assemble this complicated device?
When 'montieren' means 'anbringen' (to attach/mount), the location is often given with the preposition 'an' + dative. For example: to mount 'etwas an der Wand' (something on the wall) or 'etwas an der Decke' (something on the ceiling).
Wir müssen das neue Regal sicher an der Wand montieren.
We need to mount the new shelf securely on the wall.
When film, video, or sound is involved, 'montieren' does not mean 'zusammenbauen' (to assemble), but rather 'schneiden und zusammenfügen' (to cut and combine), i.e. to edit. The context of media production makes the meaning clear.
Die Regisseurin montiert die Schlüsselszene des Films gerade neu.
The director is currently re-editing the key scene of the film.
to build up
When putting a piece of furniture together so that it is ready to use, both aufbauen and montieren can be used. Aufbauen focuses more on the piece of furniture as a whole, while montieren emphasizes connecting the individual parts. For a finished wardrobe, aufbauen is more common; for the technical work on its parts, montieren is more suitable.

Wir montieren die einzelnen Türen und Griffe des Schranks sorgfältig.
We are carefully assembling the wardrobe's individual doors and handles.
Wir bauen den neuen Schrank nach der Anleitung im Schlafzimmer auf.
We are assembling the new wardrobe in the bedroom according to the instructions.