N5
の
Possessive use (Noun omission)
この本はたけしさんのです。
This book is Takeshi-san's.
Explanation
When a noun has already been mentioned, 「の」 can stand for it, to avoid repeating it: 「その帽子は私のです」 (That hat is mine), 「赤いのをください」 (The red one, please).
Mixed up with
It can stand for things: 「車はどっち?」 「白いのです」 (Which car? The white one.)
Be careful with people: saying 「あそこの若いの」 about an elder or a teacher is very rude; say who it is, or use 「あの方」 or 「あちらの方」.