ungestört
undisturbed
Without interruption or disturbance by other people or external influences.
Endlich hatte er einen Nachmittag, an dem er ungestört ein Buch lesen konnte.
At last he had an afternoon when he could read a book undisturbed.

undisturbed
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undisturbed
Without interruption or disturbance by other people or external influences.
Endlich hatte er einen Nachmittag, an dem er ungestört ein Buch lesen konnte.
At last he had an afternoon when he could read a book undisturbed.

The word is composed of the prefix 'un-' (not) and 'gestört' (past participle of 'stören' (to disturb)). So it literally means 'not disturbed', which is the basis for both meanings.
Bitte sorge dafür, dass ich die nächste Stunde ungestört telefonieren kann.
Please make sure that I can make phone calls undisturbed for the next hour.
In the meaning 'ohne Unterbrechung' (without interruption), 'ungestört' (undisturbed) is very often used like an adverb and then usually stands directly after the verb. It describes how an action is carried out.
Am Wochenende möchte ich einfach nur ungestört ausschlafen.
At the weekend I just want to sleep in undisturbed.
In the meaning 'harmonisch' (harmonious), 'ungestört' (undisturbed/harmonious) usually describes a relationship between people or groups. A typical combination is 'ein ungestörtes Verhältnis zu jemandem haben' (to have an undisturbed/harmonious relationship with someone).
Trotz der Scheidung haben die Eltern ein ungestörtes Verhältnis zueinander.
Despite the divorce, the parents have a harmonious relationship with each other.
quiet / calm
'ruhig' and 'ungestört' can both describe a situation in which you can work, read, or relax well. 'ruhig' mainly says that it is quiet or that there is little movement. 'ungestört' says that no one gets in the way and nothing interrupts you. A place can be quiet, but someone might still keep calling. Then you are not 'ungestört'. Learners may confuse the words because the two often occur together. Memory tip: 'ruhig' means little noise or movement; 'ungestört' means without interruption.

Meine Kollegin arbeitet zu Hause, damit sie ungestört telefonieren kann.
My colleague works from home so that she can make phone calls undisturbed.
Am Morgen ist es im Büro noch ruhig.
In the morning, the office is still quiet.