In general we are more likely to use the possessive form with people rather than things and to talk about possession rather than about other relations.
your father's car NOT the car of your father.
the beginning of the term NOT the term's beginning.
a. After a singular noun ending in s, we normally add 's: the boss's office, Chris's address. But after a surname ending in s, we can add just an apostrophe: Perkins' room/Perkins's room, Yeats' poetry/Yeats's poetry.
b. If there is a short phrase after the noun, then the possessive ending comes after the phrase.
the people next door's cat/the cat belonging to the people next door.
c. We can leave out the noun after the possessive if the meaning is clear without it.
That umbrella is my friend's.
d. Pronouns ending in one/body and the pronouns one, each other and one another can be possessive.
I found someone's coat here. They visit each other's rooms.
e. We can add an apostrophe + s to a phrase with and.
I've just been to Peter and Zoe's flat.
This is much more usual than Peter's and Zoe's flat.
f. We can sometimes use two possessive forms together.
Anita is my cousin - my mother's brother's daughter.
Source: John Eastwood, Oxford Guide To English Grammar.
