die Zerlegung
dismantling
The process in which a complex object, a machine, or a structure is taken apart into its individual parts.
Die Zerlegung des alten Motors dauerte mehrere Stunden.
The dismantling of the old engine took several hours.

decomposition / dismantling
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dismantling
The process in which a complex object, a machine, or a structure is taken apart into its individual parts.
Die Zerlegung des alten Motors dauerte mehrere Stunden.
The dismantling of the old engine took several hours.

'Zerlegung' (decomposition/dismantling) is derived from the verb 'zerlegen' (to take apart, to break down). The prefix 'zer-' expresses that something is destroyed into parts or divided up. The ending '-ung' turns it into a noun that describes the process.
Das Zerlegen alter Elektrogeräte ist ein wichtiger Teil des Recyclings.
Taking apart old electronic devices is an important part of recycling.
To say what is being taken apart or broken down, German usually uses the genitive or the preposition 'von' (of/from). Both variants are correct and common.
Die Zerlegung des alten Schrankes war komplizierter als gedacht.
The dismantling of the old cabinet was more complicated than expected.
You can recognize the exact meaning of 'Zerlegung' (decomposition/dismantling) from the context. Words like 'Motor' (engine) or 'Maschine' (machine) point to the technical meaning, 'Zahl' (number) or 'Faktor' (factor) to the mathematical one, and 'Fleisch' (meat) or 'Tier' (animal) to the craft meaning in butchery.
Für die Reparatur ist die vollständige Zerlegung des Getriebes nötig.
For the repair, the complete dismantling of the transmission is necessary.
assembly / montage
'die Montage' and 'die Zerlegung' describe opposite processes. In 'Montage', individual parts are assembled into a larger whole. In 'Zerlegung', a finished or complex object is taken apart again into its individual parts. Both words are often used with machines, furniture, or technical devices. The simple contrast is: 'Montage' puts things together; 'Zerlegung' takes them apart.

Zur Vorbereitung der Reparatur ist die Zerlegung des Motors nötig.
The engine needs to be dismantled in preparation for the repair.
Morgen beginnt die Montage der neuen Küchenmöbel.
The assembly of the new kitchen furniture begins tomorrow.