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.
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 let / to have
'jemanden in Ruhe lassen' (to leave someone alone) and 'stören' are opposites. If you leave someone alone, you do not interrupt them and you give them time or peace and quiet. If you disturb someone, you interrupt them during an activity or take away their concentration. 'in Ruhe lassen' is especially suitable when someone wants to be alone, sleep, or work. 'stören' fits when a person, a noise, or a behavior gets in the way.
Der Lehrer stört die Klasse nicht, weil sie gerade leise an der Aufgabe arbeitet.
The teacher does not disturb the class because they are quietly working on the task.
Nach dem langen Tag lässt sie ihren Bruder in Ruhe.
After the long day, she leaves her brother alone.