übernehmen
to take on
To accept and carry out a task, role, or responsibility.
Wer übernimmt die Organisation des Sommerfestes?
Who is taking on the organization of the summer party?

to take over / take on
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to take on
To accept and carry out a task, role, or responsibility.
Wer übernimmt die Organisation des Sommerfestes?
Who is taking on the organization of the summer party?

'Übernehmen' (to take over/take on) is an inseparable verb. The stress is on the second syllable (über-NEH-men), which is typical for inseparable verbs with 'über-'. The prefix always remains attached to the verb.
Sie übernimmt das Projekt von ihrem Kollegen.
She is taking over the project from her colleague.
In this meaning, 'übernehmen' (to take on) is often combined with abstract nouns that express a duty: 'Verantwortung übernehmen' (to take on responsibility), 'eine Aufgabe übernehmen' (to take on a task), 'eine Rolle übernehmen' (to take on a role), or 'die Kosten übernehmen' (to cover the costs).
Als Eltern müssen wir die Verantwortung für unsere Kinder übernehmen.
As parents, we have to take on responsibility for our children.
When it is about control, typical combinations are 'eine Firma übernehmen' (to take over a company), 'ein Geschäft übernehmen' (to take over a business), 'die Leitung übernehmen' (to take over leadership), or 'die Macht übernehmen' (to take power).
Der Konzern plant, die kleinere Firma zu übernehmen.
The corporation is planning to take over the smaller company.
When you adopt an idea or habit, the source is often given with the preposition 'von': 'etwas von jemandem übernehmen' (to adopt/take something from someone).
Diese Tradition haben wir von unseren Großeltern übernommen.
We adopted this tradition from our grandparents.
The reflexive form 'sich übernehmen' (to overdo it) has a special, negative meaning: to work too much or exert oneself too much. You can describe the effort more precisely with 'mit + dative'.
Er hat drei Jobs gleichzeitig und übernimmt sich damit total.
He has three jobs at the same time and is totally overdoing it with that.
own / peculiar
'sich etwas zu eigen machen' (to adopt something as one's own) and 'übernehmen' are close in meaning when someone uses an idea, method, or habit from others. 'übernehmen' is the simple verb for this: you take something from someone else and use it. 'sich etwas zu eigen machen' emphasizes more strongly that you truly accept it and see it as part of your own thinking or actions. 'übernehmen' often fits concrete ideas or ways of working. 'sich zu eigen machen' sounds somewhat more formal and deeper.

Du übernimmst viele gute Ideen aus dem alten Projekt.
You adopt many good ideas from the old project.
Nach dem Kurs macht sich Mehmet die neue Lernmethode zu eigen.
After the course, Mehmet adopts the new learning method as his own.