Lexical verbs express meaning in a sentence. Auxiliary verbs, on the other hand, tell us more about the lexical verb they accompany. They’re of two kinds, primary and modal.
The primary auxiliary verbs are be, have and do. Each of these can function as a main verb as well, as in I am happy, They have too much money, and I did modern languages at university. In their auxiliary role, be and have allow speakers to express further types of aspect in addition to those which can be expressed in the present tense and past tense. Do allows speakers to form questions and negatives and to add emphasis.
Here are some examples. I have walked is an instance of a perfect construction. It describes a past event that has current relevance, or one that arises from an earlier event. I am walking is an instance of the progressive aspect and describes an event that is happening now. Do you walk? asks a question. I don’t walk makes a negative statement and I do walk emphasises what we’re saying.
The core modal auxiliary verbs are can, could, may, might, will, would, shall, should and must. They can be used, among other things, to express degrees of likelihood, known as epistemic modality and degrees of permission, obligation and necessity, known as deontic modality.
Modal verbs have several characteristics. They are invariable; they are always followed by the bare infinitive of the main verb, that is, by the base form of the verb without the particle to; in negative sentences they precede the negative particle not; and they form questions to which the answer is ‘yes’ or ‘no’ by inversion, and not by using the primary auxiliary do.