
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?

to take over
To get control, ownership, or leadership of something (e.g., a company, an office).
Die junge Managerin wird die Leitung der Abteilung übernehmen.
The young manager will take over the leadership of the department.

to adopt
To pick up an idea, habit, or style from someone else and use it for oneself.
Wir haben das Konzept aus dem englischen Marketing übernommen.
We adopted the concept from English marketing.

to overdo it
To take on too much work or effort and thereby overstrain oneself.
Pass auf, dass du dich mit den vielen Projekten nicht übernimmst.
Be careful not to overdo it with all those projects.
'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.
to wear / carry
Verantwortung tragen and Verantwortung übernehmen can refer to the same task. Übernehmen emphasizes that someone is newly taking on responsibility or is being given responsibility. Tragen describes more of an ongoing state and the burden associated with it.

Ab heute übernimmt Lea die Verantwortung für das Projekt.
Starting today, Lea is taking on responsibility for the project.
Seit mehreren Jahren trägt Lea die Verantwortung für das Projekt.
Lea has been shouldering responsibility for the project for several years.