The form of the possessive/genitive case

'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
    the butcher's (shop)          the bull's horns
    a child's voice                  women's clothes
    the children's room           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 (w Mr Jones' house)      Yeats's (or Yeats') poems 

With compounds, the last word takes the's:
        my brother-in-law's guitar 

Names consisting of several words are treated similarly:
    Henry the Eighth's wives     the Prince of Wales's helicopter 

's can also be used after initials:
        the PM's secretary         the MP's briefcase the VIP's escort 

Note that when the possessive case is used, the article before the person or thing
'possessed' disappears:
        the daughter of the politician = the politician's daughter
        the intervention of America = America's intervention
        the plays of Shakespeare = Shakespeare's plays