The particle の: linking nouns and standing in for them

の links two nouns — possession, origin, kind — and can also replace the second noun once it is obvious. Both uses are here.

Also known asno particleの particlepossessive nonoun linking

N1 の N2の — linking two nouns

の particle

の joins two nouns: N2 is the main word, N1 is extra information about it (belonging, group, type). “N1's N2 / N2 of N1”.

ミラーさんは　IMCの　社員です。

ミラーさんは　IMCの　しゃいんです。

Mr Miller is an employee of IMC.

わたしは　日本語の　先生です。

わたしは　にほんごの　せんせいです。

I am a teacher of Japanese.

N2 is the main noun — the thing the phrase actually refers to. N1 is extra information that narrows it down: whose it is, which company or group it belongs to, what kind it is. IMCの社員 is a 社員 (an employee); IMC only says which employee.

The order is fixed, and it is the reverse of English “of”: extra information + の + main noun. Whatever stands last is what the phrase is about.

In the textbooksMinna I, lesson 1 Genki I, lesson 1

N の (omitted noun)の replacing a noun

の particle

When the noun after の is obvious, drop it: わたしの本 → わたしの (“mine”).

これは　わたしのです。

This is mine.

その　かさは　ミラーさんのです。

That umbrella is Mr Miller's.

If the modified noun is clear from context, you can leave it out and let の stand for it. わたしの means “my one / mine”.

In the textbooksMinna I, lesson 2 Genki I, lesson 10