的 — the possessive / modifier particle
的 is one of the most common characters in Mandarin. It glues a possessor (or any modifier) onto a noun. The pattern is: possessor + 的 + thing. 我的书 = my book. 老师的车 = the teacher's car. 她的朋友 = her friend. Order matters: the modifier always comes BEFORE the noun, and 的 sits in between like the English apostrophe-s — except it works for everything, not just possession.
The basic possessive pattern
Pronoun + 的 + noun. 我的书 (my book), 你的车 (your car), 他的家 (his home), 我们的学校 (our school). Same with full nouns: 老师的书 (the teacher's book), 朋友的家 (a friend's home), 学生的名字 (the student's name). 的 is pronounced de — neutral tone, very light.
Drop 的 with close family and tight relationships
When the noun is a close family member or a personal community, native speakers usually drop 的: 我妈妈 (my mom — not 我的妈妈), 我爸爸 (my dad), 我哥哥 (my older brother), 我妹妹 (my younger sister), 我家 (my home/family), 我朋友 (my friend — both forms are heard, but 我朋友 is common). For 'my book', 'my car', 'my teacher' — keep the 的.
的 isn't only for possession
Any modifier of a noun uses the same 的 pattern. 大的书 = a big book, 新的车 = a new car, 很好的朋友 = a very good friend. The phrase before 的 describes the noun after it. (For one-syllable adjectives in fixed pairs, the 的 is sometimes dropped — 好朋友, 小书 — but you can't go wrong by including it as a beginner.)
Asking whose: 谁的
谁 = who. 谁的 = whose. 这是谁的书? = Whose book is this? Answer: 是我的。 = It's mine. The 的 at the end of an answer doubles as 'mine/yours/his' — you don't need a separate possessive pronoun. 这是你的吗? = Is this yours? — 不是我的。 = It's not mine.
