Objective Proficiency p 45. The Genitive.

• With the name of animals the genitive is morel likely to occur with domestic animals or with those that are credited with some intelligence. E.g. A cat's tail, a dog's bark, an elephant's trunk.
• The genitive of nouns ending in -s is often formed adding 's -/ɪz/ to the noun. E.g. Mr Jones's cousin / ˈdʒəʊnzɪz/. But we sometimes find only an apostrophe, with or without the extra syllable -/ɪz/. E.g. Keats' poetry /kiːts/or /kiːtsɪz/. An apostrophe with no extra syllable is normal after Greek names, especially if they are long. E.g. Archimedes' Law /ˌɑːkɪˈmiːdiːz/
• The genitive 's is added to the last element of a compound. E.g. My brother-in-law's car. My brothers-in-law's property. The king of Spain's daughter.
• Note that you can use -'s after more than one noun. E.g. Jack and Karen's wedding. Mr and Mrs Carter's house.
• The genitive with 's is optional with inanimate nouns that refer to a group of people, to places where people live, to human institutions, etc. E.g. Africa's future. America's resources. The committee's business. The club's finances. The country's needs. The earth's surface. London's traffic. The nation's affairs.
• Apostrophe s is obligatory with nouns that refer to the length of duration of an event. E.g. A day's rest. A month (or two)'s time. A week's holiday. Julia has got three weeks' holiday. An hour (and a half)'s drive. I live near the station- it's only about ten minutes' walk.  Today's programme. A year's work.
• With time expressions you can also use the genitive. E.g. Do you still have yesterday's newspapers? Next week's meeting has been cancelled
• Apostrophe s is also obligatory in a number of fixed expressions. E.g. The ship's company. The ship's doctor. Have something at one's fingers' end (to be thoroughly familiar with). Keep someone at arm's length (to avoid having a close relationship with somebody. E.g. He keeps all his clients at arm's length.) Keep out of harm's way (in a safe place where somebody/something cannot be hurt or injured or do any damage to somebody/something. E.g. She put the knife in a drawer, out of harm's way. I prefer the children to play in the garden where they're out of harm's way.) Do something to one's heart's content (as much as you want. E.g. a supervised play area where children can run around to their heart's content). Be only a stone's throw away. Be at one's wits' end (to be so worried by a problem that you do not know what to do next. E.g. She was at her wits' end wondering how she'd manage it all in the time. The authorities are at their wits' end about juvenile delinquency.) Be at death's door (so ill/sick that you may die. E.g. I suppose you won't be coming to the party if you're at death's door!). For goodness' sake (for Christ's, God's, goodness', heaven's, pity's, etc. sake: used to emphasize that it is important to do something or when you are annoyed about something. E.g. Do be careful, for goodness' sake. Oh, for heaven's sake! For pity's sake, help me!)
• The double genitive occurs in examples like: e.g. a friend of my father's (one of the friends that my father has). That dog of Robert's (that dog that Robert has) 
• The genitive is not normally used when the noun is postmodified by a phrase or relative clause. E.g. The name of the man who came yesterday. The name of the man over there. The name of the man in the corner. What was the name of the man who phoned you?
• Classifying genitive: the genitive specifies or describes the head noun. The genitive is inseparable from the head noun. They form a unity and cannot be replaced by an of-adjunct. The genitive has the main stress. If you place an adjective or qualifying word, it refers to the group. E.g. A beautiful summer's day (describes a kind of day, even in the winter); a giant's task (a kind of task, i.e. difficult, hard);be child's play (to be very easy to do, so not even a child would find it difficult); a child's face (looks like a child); a wolf in sheep's clothing (a person who seems to be friendly or harmless but is really an enemy); a bird's eye view (a view of something from a high position looking down. E.g. From the plane we had a bird's eye view of Manhattan); a busman's holiday ( is a holiday spent by a bus driver travelling on a bus: it is no break from his usual routine. A holiday that is spent doing the same thing that you do at work.); a stone's throw (a very short distance away. E.g. We live just a stone's throw from here. The hotel is within a stone's throw of the beach.); Craftsman (a skilled person, especially one who makes beautiful things by hand. E.g. rugs handmade by local craftsmen. It is clearly the work of a master craftsman); salesman; tradesman; bridesmaid; Tuesday (Tiu: god of war and the sky); Wednesday (Woden: king of the gods); Thursday (Thor: god of thunder); a men's club; a women's college; at death's door (so ill/sick that you may die. E.g. I suppose you won't be coming to the party if you're at death's door!); hair's breadth (a very small amount or distance. E.g. We won by a hair's breadth (=by the skin of our teeth). They were within a hair's breadth of being killed); out of harm's way (in a safe place where somebody/something cannot be hurt or injured or do any damage to somebody/something. E.g. She put the knife in a drawer, out of harm's way. I prefer the children to play in the garden where they're out of harm's way). 
• We may sometimes see the apostrophe 's in plural forms not expressing possession: E.g. dot your i’s and cross your t’s: to pay attention to the small details when you are finishing a task.

  Apostrophes and plural forms

  The general rule is that you should not use an apostrophe to form the plurals of nouns, abbreviations, or dates made up of numbers: just add -s. For example: 

  MPs (e.g. Local MPs are divided on this issue.)

  1990s(e.g. The situation was different in the 1990s.)

  There are two cases in which it is acceptable to use an apostrophe to form a plural, purely for the sake of clarity:
  

  • you can use an apostrophe to show the plurals of single letters:

  I've dotted the i's and crossed the t's.

  Find all the p's in appear.

  • you can use an apostrophe to show the plurals of single numbers:

  Find all the number 7’s.

  
  Related link:
  Oxford Dictionary