Theory:

Modal Verbs are verbs that help the main verb to express one of the following:
  • Ability
  • Possibility/probability
  • Instruction
  • Permission
  • Obligation
  • Requests
  • Offer
  • Advice
The modal verbs are:
  • Shall
  • Should
  • Will
  • Would
  • Can
  • Could
  • May
  • Might
Example:
1. Shall I help you today?
2. You should always brush your teeth before going to bed.
3. Will you complete your homework on time?
4. Would you mind passing the plate?
5. Can you show me the way?
6. You could use the restroom on the right lobby instead.
7. May I know your name, please?
8. I might come for the exhibition tomorrow.
Semi-modal verbs: Some modal verbs need a preposition "to" after the verb - such modals are called Modal Phrases or Semi-modal verbs. They are a combination of modal verb \(+\) preposition.
  • Dare to
  • Need to
  • Have to
  • Ought to
  • Used to
Example:
1. How dare you come so late for the class?
2. This class needs to learn some basic discipline!
3. You have to score well to continue in my class.
4. I used to live in this city five years ago.
To summarize, take a look at the following table:
 
No.
Modal verb
Examples
1
can - to express ability.
can - to request.
could - more formal/polite request.
I can write six languages.
Can you give me some water?
Could you teach me to solve the problem?
2
cannot or cant - to express impossibility.
could not or couldn't - past impossibility.
This can't be the true report.
All of us knew it could not have happened.
3
may - to express possibility.
may - to ask permission.
It may rain today afternoon.
May I know your name, please?
4
might - to express possibility (lesser
chances of happening)
It might rain today afternoon. (Lesser chance
of rain)
5
must - to express obligation.
must - strong belief.
I must let him know about the incident.
She must be a courageous lady to do this.
6
will - to express promises.
will - to express voluntary actions.
I will wake up early hereafter.
I will make a cup of tea for you.
7
would - to express request/offer.
would - in conditional sentences.
Would you like to have some juice?
If I were you, I would have been there first.
8
should - advice.You should work out regularly to be fit.
9
shall - future action.Shall we go?