Modal Verbs (modal auxiliaries)

Modal auxiliary verbs may sound difficult but in fact they're easy. They are invariable (no conjugation). And the main verb is always the "bare infinitive" (the infinitive without "to").

Can, Could, Be able to

Can and could are modal auxiliary verbs. Be able to is NOT an auxiliary verb (it uses the verb be as a main verb). We include be able to here for convenience.

Have to, Must, Must not/Musn't

Must is a modal auxiliary verb. Have to is NOT an auxiliary verb (it uses the verb have as a main verb). We include have to here for convenience.

Shall vs Will/Should vs Would

People may sometimes tell you that there is no difference between shall and will, or even that today nobody uses shall (except in offers such as "Shall I call a taxi?"). They say the same thing about should, but it's not really true.

Would

Would is an auxiliary verb, a modal auxiliary verb. We use would mainly to talk about the past, talk about the future in the past and express the conditional mood.

Should

Would is an auxiliary verb, a modal auxiliary verb. We use would mainly to talk about the past, talk about the future in the past and express the conditional mood.

From: EnglishClub.com