die Befreiung
liberation
The act of freeing someone or something from captivity, oppression, or coercion.
Die Befreiung der Stadt wurde von der Bevölkerung gefeiert.
The liberation of the city was celebrated by the population.

liberation / release
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liberation
The act of freeing someone or something from captivity, oppression, or coercion.
Die Befreiung der Stadt wurde von der Bevölkerung gefeiert.
The liberation of the city was celebrated by the population.

The noun 'Befreiung' (liberation/release) is derived from the verb 'befreien' (to free/liberate). The ending '-ung' is a typical way to form feminine nouns from verbs that describe an action or process.
Die Befreiung der Tiere aus dem Zirkus war eine lange geplante Aktion.
The liberation of the animals from the circus was a long-planned operation.
To express what someone or something is freed from, you use the preposition 'von' followed by the dative. This structure works for all meanings of the word.
Die Befreiung von den Schulden hat sein Leben verändert.
The release from the debts changed his life.
In a historical or political context, 'Befreiung' (liberation) usually means liberation from oppression or captivity. In a personal context, it often describes a feeling of great relief.
Der Fall der Mauer war für viele eine Befreiung.
The fall of the Wall was a liberation for many people.
In this meaning, 'Befreiung' (exemption) is almost always used in connection with official obligations, rules, or costs. Typical phrases are 'Befreiung von der Gebührenpflicht' (exemption from fee obligations) or 'Befreiung vom Sportunterricht' (exemption from physical education class).
Studenten können eine Befreiung von den Rundfunkgebühren beantragen.
Students can apply for an exemption from broadcasting fees.
exception
'die Ausnahme' and 'die Befreiung' can both mean that a rule or obligation does not apply to someone. The difference is in the perspective. 'die Ausnahme' describes the special case: normally the rule applies, but not here. 'die Befreiung' describes more of an official decision that means someone does not have to fulfill an obligation, for example paying a fee or attending class. They can be confused because both involve deviating from rules. 'Ausnahme' fits better for the special situation, while 'Befreiung' fits better for the official permission.

Für die Klassenfahrt braucht Mehmet eine Befreiung von der Sportstunde.
For the class trip, Mehmet needs an exemption from PE class.
Wegen des Sturms macht die Schule heute eine Ausnahme und schließt früher.
Because of the storm, the school is making an exception today and closing earlier.