das Gesetz
law
A rule established by the state and generally binding, which all citizens must follow.
Das Rauchen in Restaurants ist gegen das Gesetz.
Smoking in restaurants is against the law.

law
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law
A rule established by the state and generally binding, which all citizens must follow.
Das Rauchen in Restaurants ist gegen das Gesetz.
Smoking in restaurants is against the law.

The word 'Gesetz' (law) is related to the verb 'setzen' (to set/place). So in a figurative sense, a law is something that has been 'festgesetzt' (set/fixed) or established as a rule.
Die Regierung hat neue Regeln für den Straßenverkehr gesetzt.
The government has set new rules for road traffic.
The context reveals the meaning: If it is about the state, politics, or punishments, the legal rule (m01) is meant. In texts about nature or science, it refers to a principle (m02). If people are talking about social groups and their behavior, an unwritten rule (m03) is meant.
Laut Gesetz der Thermodynamik geht keine Energie verloren.
According to the law of thermodynamics, no energy is lost.
In a legal context, a law is 'erlassen' (enacted), 'verabschiedet' (passed), or 'geändert' (changed/amended). You can 'verstoßen' (violate) a law or 'sich daran halten' (abide by it).
Das Parlament hat ein neues Gesetz verabschiedet.
Parliament passed a new law.
In science, people often speak of the 'Gesetze der Natur' (laws of nature), the 'Gesetz der Schwerkraft' (law of gravity), or 'physikalische Gesetze' (physical laws).
Das Gesetz von Angebot und Nachfrage bestimmt den Preis.
The law of supply and demand determines the price.
right / law
'das Recht' and 'das Gesetz' both belong to the area of rules and the state. 'das Gesetz' is a concrete rule established by the state. 'das Recht' is broader: it can be a personal right or claim, for example 'das Recht auf Urlaub' (the right to vacation), or the entire system of rules and laws. Learners often confuse the words because laws are part of law as a system. In practical terms: a 'Gesetz' is an individual rule; 'Recht' is either your right or the whole legal system.

Ein neues Gesetz verbietet das Rauchen vor der Schule.
A new law bans smoking in front of the school.
Alle Arbeitnehmer haben das Recht auf Pausen.
All employees have the right to breaks.