Not

negation

• In spoken English, not becomes n't when attached to an auxiliary which is not itself abbreviated.
  • I've not heard much. // I haven't heard much.
  • I'm not sure. // I ain't going. (ain't is fairly widespread colloquial American)

• I personally do not combine n't with may, might or shall. compare at google: couldn't // mayn't // shan't

• Usage rules are fairly strict. In formal writing abbreviations are to be avoided. The only accepted use of the apostrophe in formal writing is generally to indicate the possessive / genitive case. This is a prescriptivist, but pragmatically important, rule to know.

In written dialogue, the apostrophe is nevertheless common. An example:

Counselor: You couldn't have known that Doug wasn't coming.

Therapist: I didn't know; and I wouldn't have re-arranged my schedule if I hadn't thought he would be there.

Counselor: He hasn't been coming to those meetings for several weeks.

Therapist: I won't make the same mistake twice. Next time, if he isn't coming, I ain't going either!

Counselor: We should send the secretary a message Thursday, don't you think, just to confirm?

Therapist: Oh, you mustn't have heard, the secretary resigned yesterday.

Counselor: Oh no, he shouldn't have. I'm not surprised though. He wasn't happy about all the criticism last month. Things may not have been perfect, but at least things got done.

Therapist: Absolutely. Back to Doug again. Doesn't he have a cell phone?

Counselor: I'm not sure, I haven't got a number. I can't find his email address either.

The Therapist's cellphone rings.

Therapist: You're not going to believe this. It's Doug.

. . .

Remember: the apostrophe has two uses in English:

1. it represents a missing sound:
   • the o of not
   • the i of is (it's, he's, she's, something's, there's)
   • the a of are (You're, We're, They're)
   • the a of am (I'm (I am))
   • the ha of have, had (I've got a cold, If I'd known you were sick, ...)
   • the woul of would: (... I'd have brought chocolate. You'd like chocolate, no?)
   • the wi of will: they'll call back.
2. it represents possession:
   • Sofiane's / Luke's / Zeke's / Mohammed's / the students' notebooks.

adverb

Negations of this sort are considered to be adverbs by almost all dictionaries, like the words yes and no. Some Indo-European examples:

• nicht (Germ.)
• non (Lat.)
• pas (Fr.)
• nje (не) (Russ.)

predeterminer

Some deny the existence of determiners (articles, demonstratives, quantifiers), so the idea that a grammatical class such as predeterminers should exist is not always welcomed easily, especially by those who teach what is known in France as la grammaire scolaire.

• Not a one
• Not everybody
• not some time later (6m examples at Google, not a few of which are difficult to evaluate grammatically)
• not a few of which
• not the least of which

In any case, it is clear that the boundaries between adverbs and determination in the noun phrase (particularly deictic determination: today, tomorrow, this, that) are relatively fuzzy. At least four of the examples would clearly seem to be noun phrases.

adverb / nominal

• not even = 1. impair<i> 2. <i>même pas, selon le contexte nominal ou adverbial.