
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.

law
A fundamental principle or regular pattern in nature, science, or logic that is regarded as universally valid.
Nach den Gesetzen der Physik kann Energie nicht verloren gehen.
According to the laws of physics, energy cannot be lost.

law
An unwritten rule or strong social custom that determines behavior in a particular group or situation.
Unter Piraten galt das Gesetz, dass die Beute geteilt wird.
Among pirates, the law was that the loot would be shared.
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.
rule / period
A Regel and a Gesetz can both establish binding behavior. A Gesetz is enacted by the state and applies generally; a Regel can also be just a single requirement in an institution or group. For a state-established norm, Gesetz is therefore more precise.

Das Gesetz verlangt, dass Behörden persönliche Daten schützen müssen.
The law requires public authorities to protect personal data.
Im Amt gilt die Regel, dass Besucher ihre Handys ausschalten müssen.
The office has a rule that visitors must switch off their phones.