A の connects and related nouns.  To connect a verb or an adjective, the verb and the adjective must be nominalized.

    I.  Behind a noun:

• the owner + の + a belonging
わたしの本   my book
 
• a general location + の + a specific item
京都の大学   a university/universities in Kyoto
 
• an attribute + の + a general category
日本語の試験    a test on Japanese
 
• a specific kind + の + a general category
桃の花   plum blossoms
 
• the creator + の + the creation
ピカソの絵   Pisasso's painting
 
• color-noun + の + noun
黄色の本  a yellow book
 
• status + の + person = apposition
大学教授の横山   Yokoyama, a college professor
 
• (raw) material + の + product
木綿のスカート   a cotton skirt
 
• beneficiary + の + ため = for the sake of
家族のために毎日働いています。I'm working everyday for my family.
 
• subject of a relative clause + の = subject of the relative clause
古川さんの買った車は中古です。The car Furukawa bought is a used car.
 
※ In this sentence, 「 古川さんの買った車」is a relative clause which modifies the 車.  The main subject of this sentence is the 車.

※ If の is not followed by a noun, as in「わたしのです」, this の may be an indefinite pronoun compounding a particle の and a noun.  That is, the original phrase「 私のです」may have been「 私の (+ thing) です」originally.
 

•  verb-plain + の:  this の nominalizes the verb
小説を書くのは難しい。It's hard to write a novel.
 
• verb-plain + の + particle:  this の replaces a noun
そこにあるのが私の本です。The book over there is mine.
※ This の is a replacement of 本 (thing).
 
授業が始まるのは九時です。The time the class begins is 9 o'clock.
※ This の is a replacement of 時 or 時間 (time).
 
あそこにいるのが鈴木さんです。The person over there is Suzuki-san.
※ This の is a replacement of 人 (person).
 

• adjective-plain + の:  this の replaces a noun
その大きいのを下さい。Please give me the big one.
※ This の is a replacement of a thing.

• な-adjective + な (<--です）+ の:  this の replaces a noun
アイスクリームが好きなのは私です。The thing I like is ice cream.
<--私はアイスクリームが好きです

※の does not occur with the particles は、が、を、も、や、に.　　But it may follow other particles such as へ、から、まで、と.
父への手紙 a letter to my father
 
※の may chain together more than one nominal.
隣の女の子の犬の名前 the next-door girl's dog's name
 
※The nominalizing の cannot be used as an independent noun.  It must follow a modifying verb or adjective.

※の can replace only a noun which is understood between the speaker and the listener.

それ、わたしのです。That's mine.
 
※の may serve as a sentence-final particle.  Go to sentence-final particle no (の) page.