An auxiliary verb is a verb which cannot exist alone(1) in the verb phrase, but must be used together with a main, or lexical verb. There are two types of auxiliary verbs in English :
1) The primary auxiliaries - be, have, do
These have various grammatical functions, but no independent meaning(2).
a) Be and have combine with different forms of the main verb to create aspect :
- Be combines with the present participle to create progressive (or continuous) aspect - eg I'm going to London tomorrow (present progressive); I was hoping to see him (past progressive): I need to be doing something (progressive infinitive)
- Have combines with the past participle to create perfect aspect - eg I've finished! (present perfect); I hadn't expected you so early (past perfect); You can't have finished already! (perfect infinitive).
- Both can be used in combination to create perfect progressive aspect - eg I've been hoping to see you.(Present perfect progressive); We'd been waiting for at least an hour before he arrived (Past perfect progressive); You couldn't have been waiting that long.(Perfect progressive infinitive).
b) Be is combined with the past participle to form the passive - eg We're expected at eight: The ring was found on the beach; The application is being processed etc
c) Do is used with simple verb forms as the "dummy operator" - ie it performs the normal grammatical operations of the first auxiliary in the verb phrase for verbs which are not already preceded by an auxiliary (ie simple present, simple past) such as subject-verb inversion, negation, as a proform etc, with the lexical verb being used in the infinitive where necessary. Examples :
- Subject verb inversion in questions : I saw her / Did you see her?
- Subject-verb inversion after negative adverbs : The narrator rarely gives his own opinion / Only rarely does the narrator give his own opinion.
- To carry negation : I saw her yesterday / I didn't see her yesterday.
- As a proform : Helen doesn't know yet, but Angela does.
- To carry emphatic stress : It really did hurt.
2) Secondary, or Modal Auxiliaries
The secondary (or modal) auxiliaries are : can/could, may/might, will/would, shall/should and must. They are often all thought as "independent" verbs, but the pairs indicated for the first eight can better be considered as first and second form (or "present" and "past") variants of the same verb. They combine with an infinitive lexical verb, act as operator for the verb phrase, and, unlike the primary auxiliaries have independent meaning, always connected to the modal concepts of certainty and obligation - eg in You must be here by eight o'clock, must expresses obligation.
Form : They are defective verbs (ie do not have the full range of the normal forms), all lacking an infinitive form, a present participle and the present simple 3rd person singular form. must also lacks a second ("past") form. All are followed by the bare infinitive.
See also : modality, semi-modal verbs, periphrastic verbs
(1) Be, Have and Do can also be used as main verbs. Eg:
He was really angry - I think he's being a bit over-sensitive.
I had three interviews last week and I have another two this week.
I did a lot tody.
(2) As main verbs, they do have independent meaning, and, except for Be, when in simple forms (simple present or simple past) must always take auxiliary Do as operator in the same way as any other lexical verb. Examples :
A : Did they all do the homework?
B : Most of them didn't do it, but a few did.
A : Do you have a pen I could borrow?
B : I don't have a pen, but I do have a pencil if that's any use?
Be, on the other hand, doesn't take Do as operator for grammatical processes such as inversion or negation, but is need to form eg the emphatic of negative imperative : Do be quiet! Don't be silly!
Thornbury, S. About Language (Second edition) Cambridge