
stören
to disturb
To interrupt or hinder someone while they are doing an activity, resting, or concentrating.
Bitte stör mich nicht, ich muss diese E-Mail noch fertig schreiben.
Please don't disturb me; I still need to finish writing this email.
to disturb / bother
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to disturb
To interrupt or hinder someone while they are doing an activity, resting, or concentrating.
Bitte stör mich nicht, ich muss diese E-Mail noch fertig schreiben.
Please don't disturb me; I still need to finish writing this email.

to bother
To cause someone an unpleasant feeling or annoyance; to be perceived as annoying or inappropriate.
Stört es dich, wenn ich das Fenster öffne?
Does it bother you if I open the window?

to interfere with
To impair the function of a technical device or the reception of a signal, for example radio or Wi-Fi.
Das Gewitter stört den Fernsehempfang.
The thunderstorm is interfering with the TV reception.
The verb 'stören' (to disturb / bother) is always used with an accusative object. You ask: Whom or what does something disturb? For example: 'Der Lärm stört mich.' (The noise bothers me.) not 'mir'.
Die laute Musik stört die Nachbarn.
The loud music bothers the neighbors.
If you want to express which activity someone is being disturbed during, you use the preposition 'bei' followed by the dative.
Bitte stör mich nicht beim Lesen.
Please don't disturb me while I'm reading.
The phrase 'Stört es Sie/dich, wenn ...?' (Do you mind if ...?) is a very common and polite way to ask whether something is okay with another person.
Stört es dich, wenn ich kurz lüfte?
Do you mind if I air the room briefly?
to annoy
Stören and nerven can both express that something is bothersome. Stören is more neutral and also fits a single inappropriate action. Nerven is more colloquial and usually emphasizes irritation caused by repeated or ongoing behavior.

Das einmalige laute Tippen meines Kollegen stört mich während der Besprechung.
My colleague's one instance of loud typing bothers me during the meeting.
Das ständige laute Tippen meines Kollegen nervt mich während der Besprechung.
My colleague's constant loud typing annoys me during the meeting.