Auxiliary verb is a verb that gives further semantic or syntactic information about a main or full verb

Progressive aspect

The auxiliary verb be is used with a present participle to form the progressive aspect; for example, "I am riding my bicycle" describes what the subject is doing at the given (in this case present) time without indicating completion, whereas "I ride my bicycle" is a temporally broader statement referring to something that occurs habitually in the past, present, and future. Similarly, "I was riding my bicycle" refers to the ongoing nature of what I was doing in the past, without viewing it in its entirety through completion, whereas "I rode my bicycle" refers either to a single past act viewed in its entirety through completion or to a past act that occurred habitually.

Perfect aspect

The auxiliary verb have is used with a past participle to indicate perfect aspect: a current state experienced by the subject as a result of a past action or state. For example, in "I have visited Paris" the current state is one of having a Paris visit in one's past, while the past action is visiting Paris. The past action may be ongoing, as in "I have been studying all night". An example involving the result of a past state rather than a past action is "I have known that for a long time", in which the past state still exists (I still know it) along with the resultant state (I am someone who knew that at some past time). An example involving the result of a past state that no longer exists is "I have felt bad in the past, but not recently". The alternative use of had instead of have places the perspective from which the resultant state is viewed in the past: "By 1985 I had visited Paris" describes the 1985 state of having a prior Paris visit.

Modality

Modality means the attitude of the speaker to the action or state being expressed, in terms of either degree of probability ("The sun must be down already", "The sun should be down already", "The sun may be down already", "The sun might be down already"), ability ("I can speak French"), or permission or obligation ("You must go now", "You should go now", "You may go now"). See modal verb and English modal verb.