Title capitalization guide
Is "Not" Capitalized in a Title?

Yes — "not" is always capitalized in title case because it is an adverb.

adverb
Capitalized in 7 styles
Lowercase in 3 styles
Title Case
YES
Capitalized — adverbs are always capitalized in title case
AP Style
YES
Capitalized — adverbs are capitalized
NYT Style
YES
Capitalized — adverbs are capitalized
Chicago Style
YES
Capitalized — adverbs are principal words
MLA Style
YES
Capitalized — adverbs are always capitalized
APA Style
no
Sentence case — only first word and proper nouns
AMA Style
YES
Capitalized — adverbs are capitalized
BB Style
YES
Every word capitalized — no exceptions
Wikipedia Style
no
Sentence case — only first word and proper nouns
Sentence Case
no
Only the first word of a title is capitalized

The full answer

"Not" is an adverb and is always capitalized in title case. AP Style, Chicago Style, MLA Style, NYT Style, and AMA Style all capitalize adverbs as content words that carry meaning in a title.

The word is only three letters long, but short adverbs are capitalized just like short verbs. The principle is grammatical category: function words like articles, conjunctions, and prepositions are lowercased, while content words like nouns, verbs, adjectives, and adverbs are capitalized.

APA Style, Wikipedia Style, and Sentence Case lowercase "not" in the middle of a title. Those styles use sentence case and do not distinguish between word types.

"Not" appears in some of the most famous titles in English literature. Both instances of "Not" in "To Be or Not to Be" are correctly capitalized as adverbs in Chicago Style. "Not" is never a function word and should never be lowercased in title case.

"Not" is a negating adverb and is capitalized in all title case styles. Adverbs are content words — they modify verbs, adjectives, and other adverbs — and all major title case style guides treat them as principal words requiring capitalization.