Modal verbs are a type of auxiliary verb which express the mood of another verb.
They are used to express ideas such as: possibility, prediction, speculation, deduction and necessity.

Modal verbs have the following characteristics:

1) They do not have participle or infinitive forms
2) They do not take the ending -(e)s in the third-person singular.
3) They do not have a past form: He/she canted. He/she musted.
4) The negative is formed by the addition of not / n’t: He cannot/ He can’t. NOT He don’t can.
5) Questions are formed by inversion with the subject:  Can you? NOT Do you can?

MODAL	CONCEPT	EXAMPLE
Can	Ability: Permission: Offers:	Julie can swim. Can I come with you? ('May' is also used.) Can I help you?
Could	Possibility: Past ability: Permission: Requests:	That story could be true - who knows! Charlie could swim when he was four years old. Could I use your phone please? Could you tell me the way to the station please?
May	Possibility: Permission:	The President may come to our offices if the meeting finishes before 5 pm. May I borrow your dictionary?
Might	Slight possibility : Past form of 'may' in reported speech:	We might win a prize but I doubt it. The President said he might come.
Must	Obligation: Logical deduction:	Dogs must be kept on a lead. You must be tired after your long journey.
Mustn't	Prohibition:	You mustn't tell Alex. It's a surprise!
Should	Advice: Logical deduction:	You should take an umbrella in case it rains. I've revised so I should be ready for the test.
Ought to	Advice: Logical deduction:	You ought to write to your grandmother. 30 € ought to be enough for the taxi.
Shall	Future tense auxiliary: Offers/suggestions with ''I' and 'we':	I shall be in London on Monday (or I'll be ...). Shall I order a taxi? Shall we begin the meeting now?
Will	Future tense auxiliary: Invitations/offers:	The ticket will cost about 50€. Will you join us for coffee? Won't you come in?

*semi-modals
Semi-modal verbs are composed of two or more separate words ending with ‘to’.
Have to / have got to - be able to - ought to  are examples of semi-modal verbs.