The modals auxiliares in English are: can could, may, might, must, ought to, shall should, will, would.

MAY I/COULD I:
Are use to request permission. They are equally polite
a) May I (please) borrow your pen?
b) Could I borrow your pen (please)?

CAN I.
Is used informally to request permission, especially if the speaker is talking to someone he knows fairly well.
Can I is usually not considered as polite as may I or could I.

POR FAVOR ES NECESARIO LLEVAR ESTOS EJERCICIOS HECHOS EL PRIMER DIA DE CLASES EN ENERO. GRACIAS, Z.R. MUCHOS SALUDOS.

MIGHT:
Is also possible: Might I borrow your pen. Might I is quite formal and polite; it is used much less frequently than may I or could I.

Note:
Often the response to a po
e request consists of an action, a nod or shake of the head, or a simle "uh-huh."

WOULD YOU/WILL YOU:
The meaning of would you and will you in a polite request is the same. Would you is more common and is often considered more polite. The degree of politeness , however is often determined by the speker's tone of voice.

a) Would you pass the salt (please)?
b) Will you (please) pass the salt?

COULD YOU:
Basically, could you and would you have the same meaning. The difference is slight.
Could you and would you are equally polite.

CAN YOU:
Is often used informally. It usually sounds less polite than could you or would you.

CHANGE THE FOLLOWING SENTENCES TO INTERROGATIVE, NEGATIVE AND AFIRMATIVE WITH YES.

1. We can meet you letter.
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2. you may sit here.
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3. We should tell her about it.
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4. He may leave on Wednesday.
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5.They can go by plane.
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6.We must wait here.
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7.I can understand him easily.
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8. She should sit near the window.
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9. We must do the same thing again.
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10. She can play piano well.
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11. He can understand everything I say.
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12. You should watch television every night.
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13. She may pass her examinations.
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14. You can see him later.
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15. You may smoke here.
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16. He can meet us after lunch.
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