There are only two conditions under which you use an apostrophe in English:
I. The Genitive:
(I.1) You use an apostrophe with a possessive singular noun, whether it’s a proper
“Adrian’s fanaticism about apostrophes is tragic.”
or not, e.g.
“The computer’s battery is dead.”
(I.2) You even use an apostrophe with possessive plural nouns, e.g.
“Artists’ books are illuminating.”
“Members’ privileges have been revoked.”
(I.3) You always use an apostrophe with possessive proper names that end with an s, whether you
hear – and therefore see – the possessive s, e.g.
“You must read Marcus’s new book.”
or whether it is absent in sound and therefore in print, e.g.
“You must study Socrates’ Apology carefully.”¹
“You must read John Rawls Theory of Justice.”
is never correct in English.
(I.4) You use an apostrophe with the
impersonal possessive pronoun, e.g.
“It is not always easy to find one’s bearings.”
(I.5) You NEVER use an apostrophe with a third-person possessive pronoun. E.g.
“The mistake was hers” is right;
“The mistake was her’s” is wrong;
“It has its own source of power” is right;
“It has it’s own source of power” is wrong.
(I.6) You NEVER, EVER use an apostrophe to designate simple plurality, EVER. So, the following are
and the following are right:
so please ignore the New York Times’ practice here, because they’re wrong and it makes
them look illiterate, like Riddley Walker.
¹Thanks to Jennifer Higgie of Frieze for this sensible rule.