The dependent genitive
In this case a noun in the genitive case generally precedes another noun which is its head-word. The dependent genitive may be of two kinds:
1) the specifying genitive. It may be replaced by the of-phrase. This genitive case is used with proper names, as a rule. The common meanings are those of:
a) possession: Mary’s doll, Mary’s new doll;
b) personal or social relations: John’s wife;
c) relation of the whole to its part: the cat’s tail, the aspen’s leaves;
d) subjective relations: the doctor’s arrival = the doctor arrived;
e) objective relations: Peter’s arrest = Peter was arrested;
f) authorship: Byron’s poems;
g) the genitive of origin: the girl’s story = the girl told the story.
The specifying genitive may also be used with:
a) collective nouns: the government’s decision;
b) the names of countries, towns and continents: Britain’s population, Europe’s future;
c) the names of newspapers and nouns denoting different kind of organization: the company’s plans, the Gardian’s analysis, the Geographical Society’s gold medal, the school’s history;,
d) nouns of special interest to human activity: the mind’s activity, science’s influence, the brain’s cells;
e) such nouns as: ship, boat, car: the ship’s crew, the car’s wheel.
Note. Differentiate between the following structures containing a proper noun
used prepositively: Nelson’s tomb, the Nelson Column; Shakespeare’s birthday, the
Royal Shakespeare Theatre; Queen Victoria’s reign, the Queen Victoria Memorial;
Lincoln’s speech, the Lincoln Memorial. The noun in the genitive case denotes
possession. The proper noun in the common case denotes the name of the person to
whom something is dedicated.
2) The classifying (descriptive) genitive The noun in the genitive case here completely loses its meaning of possession and comes to denote a quality and refers to a whole class of similar objects: a girls’ school (= a school for girls), sheep’s eyes, man’s blood, a doll’s face, a doctor’s
degree, woman’s work, a soldier’s uniform.
The classifying genitive is also used with nouns denoting time and distance, such as: an hour’s trip, a moment’s delay, a week’s time, a few minutes’ silence. We don’t use the indefinite article with a plural possessive: a two-hour lecture but twohours’ lecture; a four-day journey but four-day’s journey.
This type of the genitive case is also used in set expressions: at a snail's pace, to our hearts' content, to keep out of harm's way, at my wit's end, in my mind's eye, to keep others at arm's length, by a hair's breadth, for one's country's sake, to have at one's fingers' ends, within/at a stone's throw, the lion's share.
3) The group genitive
This type is considered to be a specific feature of the English genitive case ― ’s may be added not only to a single noun, but to a whole group of words:
a) to a group of co-ordinate nouns: Jack and Ann’s house (the house belongs to Jack and Ann); cf: Jack’s and Ann’s houses (= Jack has a house and Ann has a house);
b) to an extensive noun phrase: the Prime Minister of England’s residence;
c) to a noun + possessive pronoun: somebody else’s umbrella;
d) to a group ending in a numeral: an hour or two’s walk.
Note that the group genitive is not normally used with a nominal group when the head-word is postponed by a phrase or relative clause: The name of the man walking in the street/who arrived yesterday. The independent (absolute) genitive
A noun in the genitive may be used without a head-word. It is used:
a) to avoid repetition: “Whose hat is that?” — “Virgina’s”;
b) to denote places where business is conducted: at the hairdresser’s, at the butcher’s; c) People’s houses can be referred to in this way when we are talking about the host-guest relationship: We hold a lovely evening at Peter and Helen’s. Roger was at the Watsons’ last night;
d) Firms and institutions, hospitals, churches and cathedrals often have names, ending in -s genitive. The names of firms are often written without an apostrophe: Harrods, Selfridges, Bank of Berkley’s (or Barkleys), McDonald's (or McDonalds), Marks and Spencer's (or Marks and Spencers), St Paul’s (Cathedral), St John’s (College).
There is also the double genitive. It is used when a noun is modified by two successive nouns one of which is in the genitive case and the other with the “of”- phrase: a friend of my father’s.
The noun in the genitive case must be both definite and personal: a story of Agatha Christie’s, a story of my father’s, but not: a story of a writer’s.
Note also that the noun preceding the “of” - phrase cannot be a proper noun: Mrs Brown’s Mary but never Mary of Mrs. Brown. It is important to remember that the noun preceding the “of” - phrase is premodified with the indefinite article as the meaning of the double genitive is “one
of many”: a friend of Mrs White’s, but not the friend of Mrs White’s. It is also possible to use demonstrative pronouns which presuppose familiarity: this wife of John’s, that idea of Ann’s.
More about category of case in English.