1. Modal verbs are auxiliary verbs that can not function as a main verb

2. CAN
Indicates skill or ability. In these cases it can be translated as "power" in Spanish.
EXAMPLES:
I can speak five languages
Can I have a glass of water?

3. COULD
He is the past of "can"; indicates possibility or ability in the past.
EXAMPLES:
Joe could speak english when he was young
Could you pass the salt please?

4. MAY As "could", "may" is used to indicate possibilities in the future.
EXAMPLES:
You may leave if you like.
May I leave now?

5. MIGHT
"Might" is used to indicate possibilities in the present or the future. In these cases, it is a synonym for May.
EXAMPLES:
I would bring an umbrella, it might rain later.

6. WILL "Will" is used to form the future tense.
Also the use of "will" means will or determination.
EXAMPLES:
I will help you.
Will they find a cure for cancer?

7. SHALL
The use of "shall" is much more common in the UK and is generally more polite.
EXAMPLES:
Chris shall be happy to see you.
Shall we go to the movies or a museum?

8. SHOULD
Indicates an obligation or recommendation. Reflect an opinion on what is right.
EXAMPLES:
I should call my parents more often
Should we leave a tip?

9. OUGHT TO It is synonymous with "should". EXAMPLES:
She ought to quit smoking.
They ought to work less.

10. MUST Indicates an obligation, prohibition or requirement. EXAMPLES:
You must read this book, it's fantastic.
Must you always be late?

11. WOULD To declare a preference and to ask for something politely.
EXAMPLES:
She would like to go to New York someday.
Would you like some coffee?