The Possessive Relationship

All about Possession
There is a special construction in Turkish which means - belonging to In English generally only the Possessor is marked as in - Janet's house - where the 's tells us that the house belongs to Janet. However, possession can also be marked by both the Possessor and the Possessed in English as in - the hair of the dog. In this case both words - hair - and - dog - are marked THE hair and OF THE dog.
This then is the way that Turkish uses, for both words, the Possessor and the Possessed are always marked viz: köpeğin tüyü (Köpeğ-in tüy-ü) - The hair of the dog [Lit: dog-the-of hair-the]

The Possessor

In Turkish the possessor is suffixed with -in, -ın, -un, -ün, or -nin -etc. when suffixed to a word which ends in a vowel. The -in suffix means - of, belonging to - in English, and of course is subject to vowel harmony. In grammar this is called the Genitive Case

Formation of the Possessor:

For words ending in a consonant we add -in, -ın, -un, -ün - according to Vowel Harmony Rules
adamın - (adam-ın) - the man's
adam - man - adamın - of the man, the man's
göz - eye - gözün - of the eye, the eye's

All plural forms end in a consonant -ler/-lar.
Example: adamların - (adam-lar-ın) - of the men.
adamlar - the men - adamların - of the men, the men's
fareler - the mice - farelerin - of the mice, the mice's
lastikler - the tyres - lastiklerin - of the tyres, the tyres'

Nouns ending in vowels use buffer letter -n to form -nin.
Example: banyonun - (banyo-nun) - of the bath.
banyo - bath - banyonun - of the bath, the bath's
köprü - bridge - köprünün - of the bridge, the bridge's

Formation of the Possessed

The possessed item in Turkish is suffixed with -i, -ı, -u, -ü - his, hers, its.
If the word being suffixed already ends in a vowel then the buffer letter -s- is used after this final vowel, thus the forms -si, -sı, -su, -sü are used. This suffix is also is subject to vowel harmony as shown above.
The only exception is su - water. This word historically uses the buffer letter -y- producing suyu (susu is wrong)

Formation of the Possessive Relationship

Both the Possessor and Possessed are suffixed in Turkish as follows:
The Possessor - adam - man with the Possessed - el - hand becomes:
adamın eli - [adam-ın el-i] - the man's hand, the hand of the man - (Lit: man-of hand-his.)
The Possessor - Mehmet - Mehmet - with the Possessed - palto - overcoat - becomes:
Mehmet 'in paltosu - [Mehmet-'in palto-su] - Mehmet's overcoat - (Lit: Mehmet-of overcoat-his).
So the irregular noun su - water becomes adamın suyu [adam-ın su-y-u] - the man's water.

When adding suffixes to Proper names that the suffix is separated by an apostrophe. The easy way to remember is that any noun beginning with a capital letter should be separated from its suffix. i.e. Londra - (London) - becomes - Londra'nın - London's, of London.

This Possessive Relationship is used to form Compound Nouns (Definite Noun Completion)

The Plurals of the Possessive Relationship
The plurals are formed by the addition of -ler or -lar to either the possessor or the possessed or to both according to context. The following examples should make this clear:

Both Possessor and Possessed Singular
adamın arabası - [adam-ın araba-sı] - the man's car
evin damı - [ev-in dam-ı] - the roof of the house

The Possessor Plural and Possessed Singular
yıldızların ışığı - [yıldız -lar-ın ışığ-ı] - the light of the stars
adamların arabası - [adam-lar-ın araba-sı] - the men's car

The Possessor Singular and Possessed Plural
adamın arabaları - [adam-ın araba-lar-ı] - the man's cars
odanın duvarları - [oda-nı duvar-lar-ı] - the walls of the room

Both Possessor Plural and Possessed Plural
adamların arabaları - [adam-lar-ın araba-lar-ı] - the men's cars
çocukların oyunları - [çocouk-lar-ın oyun-lar-ı] - the children's games

The Possessive Relationship in Use
The Possessive Relationship is Compound Noun in its own right and as such can have further suffixes such as -dan, -den - from, -da -de - in, on at , -a , -e - to, towards etc. - added to the Possessed item(s) to modify the meaning according to context:
Adamın arkadaşına kitabı verdim - I gave the book to the man's friend
Adam-ın arkadaş-ı-na kitabı verdim - [Lit: Man-of friend-his-to book-the gave-I]
Adamın arkadaşından kitabı aldım - I took the book from the man's friend
Adam-ın arkadaş-ı-ndan kitabı aldım - [Lit: Man-of friend-his-from book-the took-I]

Possessive Relationship Model

A note on separation of possessor and possessed

The Possessive Relationship may be separated by other words such as an adjective or an adjectival phrase:
Adamın eski arkadaşından - From the man's old friend
Adamın büyük ve pahalı arabasında - In the man's large and expensive car

Chaining Possessors
The chaining of Possessors is quite easy in Turkish, as follows:
evin kapısının penceresi - the house's door's window
And with various plural forms:
evin kapısının pencereleri - the house's door's windows
evlerin kapısının penceresi - the houses' door's window
As you can see each "chained" Possessor takes both the Possessed Suffix in -i and the Possessor Suffix in -in [hence - kapı-sı -nın - door-the-of] , while the item Possessed takes the Possessed Suffix in -i - [hence pencere-si - window-the (Sing.) or pencere-ler-i - windows-the (Plural]
Further examples of chaining:
Ali'nin defterinin sayfaları yırtılmıştır - Ali's notebook's pages are torn - [Lit: have been torn]
Bahçenin duvarlarının tuğlaları kırılmıştır. - The garden's walls' bricks are broken - [Lit: have been broken]
Mehmet'in bisikletinin lastikleri aşınılmıştır - Mehmet's bicycle's tyres are worn down - [Lit: have been worn down]
Arabamızın motorunun benzin deposunun doldurma kapağı eksiktir - Our car's engine's petrol tank's filler cap is missing - [Lit: is absent, -tir makes this definite] - Note that the -tir suffix makes these sentences have a definite meaning.

In English we would say something like:
Ali's notebook pages are torn.
The garden walls' bricks are broken.
Mehmet's bicycle tyres are worn down.
But in Turkish the "possessed nouns" have to be made definite.