der Wille
will
The mental strength or firm intention to make a decision and pursue a goal.
Wo ein Wille ist, ist auch ein Weg.
Where there’s a will, there’s a way.

will
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will
The mental strength or firm intention to make a decision and pursue a goal.
Wo ein Wille ist, ist auch ein Weg.
Where there’s a will, there’s a way.

'Der Wille' (will) is the noun related to the verb 'wollen' (to want). It describes the inner strength or intention behind the desire expressed by 'wollen'.
Er will das Projekt beenden, aber ihm fehlt der Wille, wirklich anzufangen.
He wants to finish the project, but he lacks the will to really get started.
Common collocations are 'einen starken Willen haben' (to have a strong will), 'seinen Willen durchsetzen' (to get one's way), or 'gegen seinen Willen' (against one's will). 'Die Kraft des Willens' (the power of will) is also a fixed combination.
Sie hat einen eisernen Willen und erreicht immer ihre Ziele.
She has an iron will and always achieves her goals.
The combination 'letzter Wille' (last will) is a fixed legal term for a will. The adjective 'letzter' (last) is the key clue to the meaning here.
Der Notar verlas den letzten Willen des Verstorbenen.
The notary read out the last will of the deceased.
The expression 'um … willen' surrounds a noun in the genitive. It expresses a reason or purpose and is typical of somewhat elevated language.
Um der Gerechtigkeit willen muss der Fall neu untersucht werden.
For the sake of justice, the case must be investigated again.
because of
'wegen' and 'um ... willen' can both express a reason. 'wegen' is the normal preposition when you simply say why something happens. 'Um ... willen' is a fixed expression and sounds more strongly like purpose, consideration, or 'for someone's sake'. Learners may confuse them because both often have to do with a reason. A practical way to remember it: for a normal reason, you usually use 'wegen'. If you want to say that you are doing something for someone or for an important goal, 'um ... willen' fits better.

Um der Kinder willen streiten die Eltern nicht vor ihnen.
For the sake of the children, the parents do not argue in front of them.
Wegen des starken Regens bleibt der Markt heute geschlossen.
Because of the heavy rain, the market will remain closed today.