Can

The modal auxiliary can is used

Expressing ability

to express ability (in the sense of being able to do something or knowing how to do something):

    Ramu can run faster than anyone I know.

    I can speak Chinese.

    Can your brother speak english?”

    I don’t think he can speak english.”

    do the best you can.”

    When can you start?”

Permission

to expression permission 

    I can drive Ramu's car when he is abroad.

    Can Gopi come to the function with us?

    You can leave the classroom once you are finished with the test.

    You can’t have any dessert until you’ve finished your dinner.

permission 

can or may?

The only difference between the two verbs is that one is more polite than the other. In informal contexts it’s perfectly accepatable to use can; in formal situatioons it would be better to use may.

Can 

Compare

asking for permission	formal/polite?	giving permission	formal/polite?
Can I ask you a few questions?”	informal	Yes, Gopi can. Yes, you may. Yes, you could.	informal
Could I ask you a few questions?	more formal/polite		formal/polite
May I ask you a few questions?	even more formal/polite

Making requests

       Can I have a glass of water?

       Your sister is a lawyer, right? Can she give me some legal advice?

        Can you give me a lift to school?

Requests usually refer to the near future.( in an informal way, especially between friends or family ). ( Informal Request )

    It is common to use can to make a request of someone. For example:

    Can I have a glass of water?

    Can you hand me the pen?

In more formal or polite circumstances, we can use other modal verbs such as could or would to create more polite constructions, as in:

        Would you please be quiet?

        Could you help me with this assignment?

Making offers(informal)

While it might be seen as impolite to use can to make a request, it is perfectly polite to use it to                 make an offer. For example:

        Can I help you?

        Can I do anything to help get dinner ready?

        Can I help you find what you need?

        There is nothing left in the fridge. Can I do some shopping for you?

If we want to be even more polite or add formality to the offer, we can use may instead, as in:

        May I be of some assistance?

        May we help you in any way?