Modals

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The modals May, shall, would, could, can and will are all used to offer or request something; the choice depends on the degree of formality or politeness required. Modal auxiliaries are never conjugated. They are always followed by a main verb in the base form (without to). Modal auxiliaries do not require another auxiliary to form questions and negatives. Simply add not or invert the subject and the modal.

May / Shall May and shall are formal and very polite. Only use them with I and we. Shall I help you with your coat, madam?
May I ask you not to smoke inside, sir?
Would Would is used for formal, polite offers and requests. Would you sign this form for me?
Would you like me to explain the procedure?
Could / Can Could and can are polite but more informal. Could you tell me where to find the paper supplies?
Can you show me the confirmation e-mail?
Will Will is the most informal way to make a request or offer. Will you pass me the stapler?
Hang on; I will give you the Wi-Fi password.

How may I help you? – Grammar