Mind can mean ‘dislike’, ‘be annoyed by’, ‘object to’. We use mind mostly in questions and negative sentences.

    I don’t mind you coming in late if you don’t wake me up.
    Do you mind the smell of tobacco?’ ‘Not at all. ‘

Do you mind . . . ?and Would you mind . . . ?are often used to ask for permission, or to ask people to do things. We can use -ing forms or if-clauses.

    [Do you mind/Would you mind. .. -ing. .. ?]
    Would you mind opening the window? (- Please open the window.) Would you mind my opening the window? (= Can I open the window?)
    Do you mind people smoking in the kitchen?
    Do you mindAA/ould you mind if… ?
    Would you mind if I opened the window?
    Do you mind if people smoke in the kitchen?
    Do you mind if I smoke?’ ‘No, please do.’

Note that the answer ‘No’ is used to give permission after Do you mind …?(/ don’t mind means ‘I have nothing against it; it’s all right’.)