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 (semi-modal)	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-MODAL VERBS:
Semi-modals are a subcategory of modal verbs.
They are sometimes called 'quasi-modal', 'semi-auxiliary', or 'marginal modal'.
Semi-modal verbs sometimes act as modals and sometimes as full main verbs, hence the name 'semi-modal'.
The main semi-modal verbs in English are 'ought to', 'have to', 'have got to', 'used to', and 'need to'.
Also considered as semi-modals are : ‘dare’, ‘had better’ and ‘be able to’.

Negative and Question Forms of Semi-Modal Verbs:
Unlike modal verbs, the negative and question forms of semi-modal verbs are similar to those of ordinary verbs, i.e. 'don't', 'doesn't', or 'didn't' for negatives, and 'do' or 'did' for questions.

Modal :
You must leave now.
You mustn’t leave now. (you don’t must…)
Must you leave now ? (do you must ?)

Semi-modal :
You have to leave now.
You don’t have to leave now.
Do you have to leave now ?