Will is best known as an indicator of future tenses.  There are many ways to express the future – including using other modals – but most of them express some level of certainty, ranging from uncertain to confident.  (This is a big part of what the term ‘modality’ entails.)  One possible reason that will is so popular here is that it largely removes the speaker’s opinion or certainty level and states the verb phrase as if it is a near truth.  Would does the same for unreal situations.

The other way will and would are used is to reveal habits, and once again, they do so matter-of-factly.

Different coursebooks and other references use different terms for various groups of modals.  These might not align with the names of the flavors as shown in this video, but you should probably recognize some of those terms in the sub-groupings shown toward the bottom of the diagrams.

Modals of Ability and Habit are made past a different way; they rely on their pairs.  Could, might, should, and would are the past forms of can, may, shall, and will, respectively.

When those past forms are followed by have, they take on an unreal meaning.  (For example, we could use ‘could’ for a real past ability, but ‘could have’ for a hypothetical past ability).

There are some dialects which allow double modals – that is, two adjacent modals, as long as they express different flavors.  For example, “I might could fix that sink for you.”  The first modal (‘might’) expresses possibility while the second modal (‘could’) expresses ability.

However, most dialects do not allow double modals.  So to express modality in those two flavors, the speaker would have to replace the second modal with a phrase that is not defective.  The best alternative here is: “I might be able to fix that sink for you.”

Auxiliary Verbs have a particular order they adhere to when there are multiple ones (serving different purposes) in a verb string.  It turns out that the modal verb should always come before any other auxiliary verb, like HAVE or BE (if a modal is included at all).

This means that when there is a modal verb, it carries all the duties of the Leading Auxiliary, like pairing with not, coming before the subject in inverted situations like questions, and representing the full verb string in ellipses (as with short answers).