What Follows Auxiliary Verbs?

A. Auxiliary verbs followed by a verb ending in -ing or -ed:

The boy is flying a kite.
The book was listed as a best seller.
The boy has closed the window

B. Auxiliary verbs followed by the basic form of the verb:

Modal auxiliaries, do in question/negative sentences, or emphatic do infinitive
Paul may arrive tomorrow.
Do you like fish?
I do believe that he is right
He does not like playing cards.

Meaning of Key Auxiliary Verbs

A. Will: be willing to; intend to

I will open the door for you.
I will be there at 8:oo.

B. Shall: intend to (formal); have decided to

Where shall we sit?
We shall ask the committee.

C. May Can: be possible to do

Can fish live in the river?
It may rain tomorrow.

D. Can Could May: be allowed to do

May I have one?
You can take both of them.

E. Must: be necessary; be logically certain

Note: negative cannot/can't, must not
It must be her purse.
This step must be next.

F. Must Have to: be required to do

Everyone must be on time.
They have to work late

G. Should /Ought to Had better: be obliged to do

You should call her.
We ought to get there early.

H. Should have Could have p.p.: was not true; did not happen

She should have read the book.
They could have won, but they didn't

I. Used to Would: did in the past

We used to talk every day.
In the spring, I would plant flowers.

Source: Starter_TOEIC_3rd_Edition