Three modal verbs are commonly used when asking for permission:

You can use the modal verb 'can' to ask for permission; however, this is an informal way of asking for permission and is used in casual contexts. For example:

Using 'may' is a more polite and formal way to ask for permission. Accordingly, this is the proper way of asking for permission when talking to someone in a position of authority. Here are some examples:

The modal verb 'could' is the past tense of 'can.' However, this does not mean that it always refers to a time in the past. It can be used as a more indirect or polite way of asking for permission. For example:

This expression is used to ask for permission or, more specifically, to ask if doing something bothers anybody. In this case, no authority is involved; it is only a matter of courtesy and consideration of other people's convenience and preference. Here are some examples:

Out of the three modals discussed above that are used to ask for permission, 'can' and 'may' can be used to give permission as well. For example:

There are some phrases and expressions that are used to give permission to others in a polite way. Here we have some of them on the list.

Check out the dialogues to see how they are used:

There are some phrases and expressions that are used to reject someone's request for permission politely. For example:

Check out the dialogue to see how these are used: