〜くない

〜くない is the negative for i-adjectives — "isn't X." 寒い → 寒くない = "isn't cold." Pattern: drop the final い, add くない.

Same trap as 〜かった: English-mind expects 寒いじゃない ("isn't cold") by analogy with 学生じゃない. Don't — i-adjectives have their own negative morphology. 寒いじゃない is wrong (or at best a colloquial sentence-final contradiction marker, which is a different construction).

The negative form 〜くない itself behaves like an i-adjective. It can take past (〜くなかった = "wasn't cold"), te-form (〜くなくて), and so on. Adding です gives polite-register: 寒くないです.

The いい exception applies here too: いい negates to よくない, not いくない. Past negative: よくなかった. Memorize the よ- stem once and the rest of the tense paradigm follows.

Na-adjectives and nouns use じゃない / ではない instead: 静かじゃない ("isn't quiet"), 学生じゃない ("isn't a student"). The split between i-adjective conjugation and noun/na-adjective copula conjugation is a core grammatical line in Japanese.