What is a Primary Auxilary and an Modal Auxilary?(the chapter is actually wrong)

Auxiliary verbs are helping verbs. They help the main verbs in a sentence.

For example: He is eating an apple.

'is' is the helping verb to the main verb 'eating'

There are three Primary auxiliaries in English: do, be, have. They help in many types of sentence construction, but do not 

have much meaning themselves. They are used as 'does, did, do, is, was, am, were, has, have, had, etc'.

The modal auxiliaries are also helping verbs that express modality, i. e., ability, permission, likelihood and obligation.

For example: can, could, will, would, should, may, might, etc. are all modal auxiliaries.

Remember-modals are never combined with primary auxiliaries. If a negative is to be made, it is done by adding 'not'- We should not do things to hurt our elders.

Modals never change form, i. e., -s or -es is not added to them(as it can be added to 'do')