
adoptieren
to adopt
To legally accept a child as one's own and take them into one's family.
Sie haben beschlossen, ein Kind aus dem Waisenhaus zu adoptieren.
They decided to adopt a child from the orphanage.
to adopt
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to adopt
To legally accept a child as one's own and take them into one's family.
Sie haben beschlossen, ein Kind aus dem Waisenhaus zu adoptieren.
They decided to adopt a child from the orphanage.

to adopt
To take in an animal, usually from an animal shelter, and become its owner.
Wir wollen am Wochenende einen Hund aus dem Tierheim adoptieren.
We want to adopt a dog from the animal shelter this weekend.

to adopt
To take on and use an idea, method, or style from someone else.
Das Unternehmen hat die neue Marketingstrategie aus den USA adoptiert.
The company adopted the new marketing strategy from the US.
Verbs that end in '-ieren' often come from other languages. They are always regular and form the perfect tense with 'haben' and the past participle ending in '-t', but without the prefix 'ge-'. So it is 'hat adoptiert' (has adopted).
Meine Tante hat vor vielen Jahren ein Kind adoptiert.
My aunt adopted a child many years ago.
The direct object of the verb makes the meaning clear. You either adopt a living being ('ein Kind' = a child, 'einen Hund' = a dog) or something abstract ('eine Idee' = an idea, 'eine Methode' = a method, 'einen Lebensstil' = a lifestyle).
Viele Firmen adoptieren agile Arbeitsmethoden, um flexibler zu sein.
Many companies adopt agile working methods in order to be more flexible.
When naming the place of origin of an adopted child or animal, the preposition 'aus' (from) is used. Typical formulations are 'ein Kind aus einem anderen Land adoptieren' (to adopt a child from another country) or 'einen Hund aus dem Tierheim adoptieren' (to adopt a dog from the animal shelter).
Sie möchten eine Katze aus dem örtlichen Tierheim adoptieren.
They would like to adopt a cat from the local animal shelter.
to take over / take on
When it comes to someone else’s method, übernehmen and adoptieren can both express using it as one’s own approach. Übernehmen is neutral in this context. Adoptieren more strongly emphasizes the conscious decision to accept the method and apply it oneself.

Nach langer Prüfung adoptiert das Team bewusst die Methode der anderen Abteilung.
After careful consideration, the team consciously adopts the method used by the other department.
Das Team übernimmt die erfolgreiche Methode der anderen Abteilung.
The team is adopting the successful method used by the other department.