Would you mind…?
What it really means
The standard polite request form: "Would you mind opening the window?" Note the confusing answer: "No, not at all" means YES, I will do it. Saying "yes" would literally mean you DO mind and refuse.
Context, tips & common mistakes
The polarity trap in the answer catches learners for years: because the question literally asks "would it bother you?", the helpful answer is negative — "no, not at all", "of course not" — and a cheerful "yes!" technically means refusal. In practice Britons soften genuine refusals into full sentences ("actually, I'd rather you didn't — sorry"), so a bare "yes" or "no" is rarely heard; copy that habit and you cannot go wrong. Watch the two related forms: "do you mind if I…?" asks permission for yourself (answer "go ahead"), while "would you mind doing…?" asks the other person to act. The past form "would you have minded" is rare; but "if you wouldn't mind" tacked on the end of an instruction ("close the door on your way out, if you wouldn't mind") is a polite order, not a question. Tone matters too: an icy, over-enunciated "would you MIND?" — on a train, about your phone volume — is a complaint, and the right response is an apology, not "not at all".