die Bereitschaft
willingness
The inner attitude of being ready or willing to do something specific.
Seine Bereitschaft zur Zusammenarbeit hat das Projekt gerettet.
His willingness to cooperate saved the project.

readiness / willingness
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willingness
The inner attitude of being ready or willing to do something specific.
Seine Bereitschaft zur Zusammenarbeit hat das Projekt gerettet.
His willingness to cooperate saved the project.

The word derives from the adjective 'bereit' (ready). The ending '-schaft' turns the adjective into a noun that describes a state or quality.
Er ist bereit zu helfen, also zeigt er Hilfsbereitschaft.
He is ready to help, so he shows a willingness to help.
To express what someone is willing to do, the construction 'die Bereitschaft zu + Infinitiv' is almost always used. Alternatively, 'für + accusative' can also be used.
Die Bereitschaft, neue Dinge zu lernen, ist sehr wichtig.
The willingness to learn new things is very important.
In the sense of 'Wille' (will/willingness), 'Bereitschaft' is often combined with verbs such as 'zeigen' (to show), 'erklären' (to declare), or 'bekunden' (to express). Typical adjectives are 'groß' (great), 'hoch' (high), or 'gering' (low).
Der Politiker zeigte große Bereitschaft zum Kompromiss.
The politician showed a great willingness to compromise.
In a professional or emergency context, the fixed expressions 'in Bereitschaft sein' (to be on standby) or 'sich in Bereitschaft halten' (to keep oneself on standby) are often used. This means being ready for immediate deployment.
Die Feuerwehrleute sind während ihrer Schicht rund um die Uhr in Bereitschaft.
The firefighters are on standby around the clock during their shift.
When a 'Bereitschaft' is referred to as a countable unit, for example in the plural 'die Bereitschaften', it always means a concrete group of people, usually from the police or emergency services.
Zwei Bereitschaften der Polizei sicherten das Stadion ab.
Two police standby units secured the stadium.
will
'Wille' and 'Bereitschaft' can both express that someone wants to do something or is able to do something. 'Wille' emphasizes the firm inner decision and the strength to pursue a goal. 'Bereitschaft' emphasizes more that someone is ready to do something, to help, or to be available. That is why they can be confused, especially in sentences like 'Er hat den Willen' (he has the will) and 'Er zeigt Bereitschaft' (he shows willingness). When it is about strong personal determination, 'Wille' fits. When it is about openness, help, or availability, 'Bereitschaft' is more natural.

Nach dem Unfall zeigte die Nachbarin große Bereitschaft zu helfen.
After the accident, the neighbor showed great willingness to help.
Mit starkem Willen hat Mehmet die Prüfung beim zweiten Versuch bestanden.
With strong will, Mehmet passed the exam on his second attempt.