の (the one)

の can stand in for a noun that's obvious from context, like "one" in English: 赤いのをください, "I'll take the red one"; もっと安いのはありますか, "do you have a cheaper one?"

It follows い-adjectives and plain verbs directly: 大きいの, 昨日買ったの ("the one I bought yesterday"). な-adjectives keep their な: 静かなの.

After a noun, it's the possessive の you already know, with the second noun dropped: 私のです, "it's mine".

もの ("thing") does the same job more formally, and やつ more casually. Pointing at something in a shop and saying これと同じのをください, "the same one as this, please", is a handy use.