Most modal verbs are "pure" modal verbs, e.g. may, can, might, should, must, and shouldn't.

Other modal verbs such as, have to, need to, and ought to are known as semi-modal verbs as they have similar functions to pure modals (ability, obligation, etc.) but they don't follow the same form rules as "pure" modals.

Why Do We Use Modal Verbs?

Modal verbs by themselves don't mean anything, but in a sentence/context we use them to express certainty, possibility, impossibility, permission, obligation, ability, deduction, and to make requests, invitations, and offers.
One of the main challenges for learners is that modal verbs have a variety of meanings and uses:

I can speak Portuguese - Ability

Can I go to the bathroom? - Permission

In an exam you must be silent - Obligation

Shamali must be in the gym because she's not here and nor is her gym bag - Deduction

Can, can’t 

We use can + infinitive without to.

I can cook. 

I can to cook. 

We can’t go there. 

We can’t to go there. 

Don’t use -s after he/she/it

We don’t add -s after he/she/it. 

He can cook. 

He cans cook. 

Don’t use do/don’t

Can is an auxiliary verb and has a negative and interrogative form. We don’t use “do/don’t” to make questions and negatives.

Can you cook? 

Do you can cook? 

He can’t cook. 

He don’t can cook. 

Can, can’t – Use

Ability

We use can/can’t to talk about ability in the present.

Dana can cook very well. 

I can’t speak Italian. 

Possibility

We use can/can’t to ask for permission or to say if something is possible or not.

Can I come with you?

You can’t drink wine you are taking pills. 

He is in Rome so he can’t come to our meeting. 

Ask for something

We use can/can’t to ask for something and to order in bars, restaurants, shops, etc.

Can you give me your red dress for the party?

Can I have some coffee, please? I had tea this morning so I need a coffee right now.

Can I have a coffee to go, please?

Should(n’t) + infinitive

Should is a modal verb, and all modal verbs are followed by an infinitive (without to).

You should to go to Emma’s party tomorrow. 

You should go to Emma’s party tomorrow. 

Should not= shouldn’t

The negative form of should is should not or shouldn’t.

You should not go on this trip alone. = You shouldn’t go on this trip alone. 

Questions

To ask questions, we use should + subject + infinitive. We don’t use the verb do to ask questions.

Do we should invite them to our home? 

Should we invite them to our home? 

Should, shouldn’t 

Giving advice

We use should or shouldn’t to give somebody advice and to say what is or isn’t the right thing to do.

You look bored. You should go to the cinema with your friends.

He shouldn’t drink. He is still very young. 

I think you should …

We often say I think … should … to give somebody advice.

I think you should buy that house if you’ll move in with your boyfriend. 

I think we should go to that party; it could be fun. 

In a negative sentence, we often say I don’t think… should… (NOT I think… shouldn’t…)

I think you shouldn’t tell him yet; he’s very sad. 

I don’t think you should tell him yet; he’s very sad. 

We often say Do you think … should … to ask for advice.

Do you think I should look for another house, a larger one maybe?

Ought to, ought not to

We can also use ought to instead of should and ought not to instead of shouldn’t.

You ought to have some breakfast, you have a busy day today.

He ought not to eat so fast. 

Might (not)= Maybe it is (not) true

We use might/might not when we think something is (not) or will (not) be true, but we aren’t sure.

Mom isn’t here. She might be in the kitchen.

The payment went through. I might actually be able to pay that bill this afternoon. 

They might win the competition if they study hard. 

I might (not)= It is possible that I will (not)

We say that someone might do something to mean that ‘it is possible that someone will do something‘.

I might go visit my grandma this week. I miss her.

Jane might come to the party.

We say that someone might not do something to mean that ‘it is possible that someone won’t do something‘.

I might not buy that house. It’s too expensive for us now.

He might not go to the mall today. He is very busy 

May, may not

May = might

We can use may and may not instead of might and might not.

Susan may be late for our yoga class today. 

My parents may not like what I bought for their anniversary. 

May I…?

We don’t often use might or may in questions. However, we can use may I in questions to ask for permission.

May I sit here? (=Can I sit here?)

May I come in?

We can use both may and might

To indicate possibility in the future

We can use may or might + infinitive to indicate possibility in the future: to say that maybe something will happen or someone will do something.

It may take too long to get there on foot so let’s take the car.

He might be late to the party.

We use may not or might not + infinitive when we want to express negative possibility in the future: to say that maybe something will not happen or someone will not do something.

My sisters may not go on holiday to Rome.

My sisters might not go on holiday to Rome.

To speculate about the present

We can also use may or might + infinitive to speculate about the present: to say that maybe something is true.

I think they may have my check by now.

I think they might have my check by now.

We use may not or might not + infinitive to say that maybe something is not true in the present.

Jude may not be at work today, he had some personal issues. 

Jude might not be at work today, he had some personal issues. 

We use may and NOT might

To give, deny, or ask for permission

We use may and may not to give and not give someone permission to do something. Might is not used in this context.

You may sit here if you like. 

You might sit here if you like. 

You may not open the dictionary in the classroom. 

You might not open the dictionary in the classroom. 

We can also use may in questions to ask for permission.

May I ask for yor help?