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 | Quiz
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/Mustn't | Quiz
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 versus Will | Should versus 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 | Quiz
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 | Quiz
Should is an auxiliary verb, a modal auxiliary verb. We use should mainly to give advice or make recommendations, talk about obligation or talk about probability and expectation.