The form of the possessive/genitive case

What should I use? "'s form" or "of sthg form" to express possession?
Here is the answer:
's
- A 's is used with singular nouns and plural nouns not ending in s:
► a man 's job
► the people 's choice
► men' s work
► the crew' s quarters
► a woman' s intuition
► the horse' s mouth
► Russia 's exports

- A simple apostrophe (') is used with plural nouns ending in s:
► a girls' school
► the students' hostel
► the eagles' nest
► the Smiths' car

- Classical names ending in s usually add only the apostrophe:
► Pythagoras' Theorem
► Archimedes' Law
► Sophocles' plays

- Other names ending in s can take 's or the apostrophe alone:
► Mr Jones 's (or Mr Jones' house)
► Yeats 's (or Yeats ') poems

of + noun:

- When the possessor noun is followed by a phrase or clause:
► The boys ran about, obeying the directions of a man with a whistle.
► I took the advice of a couple I met on the train and hired a car.

- With inanimate 'possessors', except those listed in above:
► the walls of the town
► the roof of the church
► the keys of the car

- It is often possible to replace noun X + of + noun Y by noun y + noun X:
► the car keys

- The first noun becomes a sort of adjective and is not made plural:
► the roofs of the churches = the church roofs

Unfortunately noun + of + noun combinations cannot always be replaced in this way and the student is advised to use of when in doubt.

Sources: A Practical English Grammar. Thomson & Martinet. Oxford University Press, 1986.