die Aneignung
acquisition
The process of acquiring knowledge, abilities, or skills and making them one's own.
Die Aneignung einer neuen Sprache erfordert viel Zeit und Geduld.
The acquisition of a new language requires a lot of time and patience.

acquisition / appropriation
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acquisition
The process of acquiring knowledge, abilities, or skills and making them one's own.
Die Aneignung einer neuen Sprache erfordert viel Zeit und Geduld.
The acquisition of a new language requires a lot of time and patience.

'Aneignung' (acquisition/appropriation) is the noun corresponding to the reflexive verb 'sich (etwas) aneignen' (to acquire/appropriate something). The verb describes the active process of making something one's own and is always used with an accusative object.
Er hat sich in kurzer Zeit umfassende Kenntnisse angeeignet.
He acquired extensive knowledge in a short time.
In the context of learning, 'Aneignung' (acquisition) is often used with the preposition 'von' (of) or a genitive to specify what is being learned. Typical phrases are 'die Aneignung von Wissen' (the acquisition of knowledge), 'die Aneignung von Fähigkeiten' (the acquisition of skills), or 'die Aneignung einer Sprache' (the acquisition of a language).
Die Aneignung von Fachwissen ist für diese Position unerlässlich.
The acquisition of specialist knowledge is essential for this position.
This meaning is often found in legal or formal contexts. A clear signal word is the adjective 'widerrechtlich' (unlawful), which describes an illegal taking of possession.
Ihm wird die widerrechtliche Aneignung von Firmeneigentum vorgeworfen.
He is accused of the unlawful appropriation of company property.
In social debates, this word is used almost exclusively in the fixed collocation 'kulturelle Aneignung' (cultural appropriation). This refers to the adoption of symbols or practices of another culture.
Der Designer wurde für die kulturelle Aneignung traditioneller Muster kritisiert.
The designer was criticized for the cultural appropriation of traditional patterns.
possession
'der Besitz' and 'die Aneignung' both have to do with something coming to someone or being under someone's control. 'Besitz' describes more of a state: something belongs to someone, or someone actually has it with them or under their control. 'Aneignung' describes more of a process: someone takes possession of something or makes it their own. This is why the words can be confused when talking about things and property. In practical terms: after 'die Aneignung' (appropriation), something can be in a person's possession.

Die Aneignung des fremden Fahrrads war nicht erlaubt.
The appropriation of someone else's bicycle was not allowed.
Nach dem Umzug war fast der ganze Besitz der Familie in Kartons verpackt.
After the move, almost all of the family's possessions were packed in boxes.