Modal verbs

The modal verbs include can, must, may, might, will, would, should. They are used with other verbs to express ability, obligation, possibility, and so on. Below is a list showing the most useful modals and their most common meanings:

Modal	Meaning	Example
can	to express ability	I can speak a little Russian.
can	to request permission	Can I open the window?
may	to express possibility	I may be home late.
may	to request permission	May I sit down, please?
must	to express obligation	I must go now.
must	to express strong belief	She must be over 90 years old.
should	to give advice	You should stop smoking.
would	to request or offer	Would you like a cup of tea?
would	in if-sentences	If I were you, I would say sorry.

Modal verbs are unlike other verbs. They do not change their form (spelling) and they have no infinitive or participle (past/present). 

The modals must and can need substitute verbs to express obligation or ability in the different tenses. Here are some examples:

Past simple	Sorry I'm late. I had to finish my math test.
Present perfect	She's had to return to Korea at short notice.
Future	You'll have to work hard if you want to pass the exams.
Infinitive	I don't want to have to go.

Past simple	I couldn't/wasn't able to walk until I was 3 years old.
Present perfect	I haven't been able to solve this problem. Can you help?
Future	I'm not sure if I will be able to come to your party.
Infinitive	I would love to be able to play the piano.

Modals are auxiliary verbs. They do not need an additional auxiliary in negatives or questions. For example: Must I come? (Do I must come?), or: He shouldn't smoke (He doesn't should smoke).

A quiz on modals:

http://esl.fis.edu/grammar/multi/modal1.htm