The apostrophe is a punctuation mark in the Latin and some other alphabets. It is used to indicate quotations, to show that one or more letters are left out (contractions), to show the possessive form (genitive) of names and nouns, and to mark the plural of single letters.

QUOTATION

In UK English, single quotation marks are commonly used (even if the US English system is also accepted), while US English prefers double quotation marks.

UK English: ’Welcome to London’, he said.

US English: A man appeared in the doorway asking, ”Is there a restroom somewhere here?”

When a quote appears inside another quote, the opposite style of quotation marks is used:

UK English: The woman looked at the policeman and said, ’All I heard was ”I can’t find my keyes”’.

US English: The woman looked at the officer and said, ”All I heard was ’I can’t find my keyes.’”

CONTRACTION

In a contraction, an apostrophe represents one or more letters that have been omitted.

I’ve  I have
I’d  I had or I would
He’s  He is
They’re They are
She can’t She cannot
You mustn’t You must not
Singin’ in the rain Singing in the rain
O’Leary  [descendant] of Leary
Rock’n’roll  Rock and roll

An apostrophe can represent thousand:

15’ = 15 000

An apostrophe can replace the first two numbers in a year:

This was popular in the ’80s = in the 1980s

POSSESSIVE

An apostrophe is used with an s after names or nouns to show ownership or close connection.

This is the boy’s room
Let me introduce my wife’s best friend

In the plural, there is no s after the apostrophe:

This is the boys’ room

Especially in spoken language, the plural is expressed using of: This is the room of the boys.

A sign outside a bar with the word cocktail's. The use of an apostrophe is wrong.
Not quite right…

PLURAL OF LETTERS

An apostrophe is used to mark the plural of single letters:

It’s hard to distinguish between your g’s and q’s.

Mind your p’s and q’s (be careful about what you say or do).

 Don’t confuse an apostrophe with an accent! Read more here.