Theory:

Modal verb is an auxiliary verb that expresses necessity or possibility.
An Auxiliary verb is a helping verb used with a main verb to form a verb phrase. It indicates tense, mood, grammatical aspects of the main verb.
 
Modals are also known as modal auxiliary verb. 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.
Modal verbs from the lesson "A Bicycle in Good Repair":
  1. Don’t do that; you will hurt it.
  2. You will make yourself tired.
  3. We may as well see what is the matter with it.
  4. He then said that while he was about it he would see to the chain for me.
  5. Now he would see to the chain.
  6. He tightened it till it would not move.
  7. At the end of ten minutes, I suggested he should hold the fork.
  8. I should handle the wheel.
  9. A child might have noticed it.
  10. He said it would do for the present.
  11. One moment the bicycle would be on the gravel path.
  12. The position would be reversed.
  13. But his triumph would be short-lived.
  14. I think that will do.
 
Examples of sentences containing "must", "should", or "ought to" from the lesson:
  1. We must put back all we can find.
  2. We mustn’t lose any of them.
  3. We should go for a long bicycle ride.
  4. I felt much as I should had he started whacking my dog.
  5. I did not see why he should shake it.
  6. I should handle the wheel.
  7. I suggested he should hold the fork.
  8. I ought to have been firm.