Based on The Chicago Manual of Style (sixteenth edition)

Singular nouns: Add an apostrophe and an s.

Plural nouns (regular): Add an apostrophe only.

Examples: the girl’s car; the girls’ cars.

This general rule also applies to singular and plural forms of proper nouns, including names ending in s,x, or z, even if these letters are unpronounced.

Examples: James’s house; Marx’s writings; Jesus’s teachings; Berlioz’s works; Camus’s early work; Descartes’s philosophy.

Classical names (same rules apply): Euripides’s tragedies; the Ganges’s source; Xerxes’s armies.

EXCEPTIONS

Possessive of nouns plural in form, but singular in meaning (including the name of a place, organization or publication): Add an apostrophe only.

Examples: politics’ true meaning; this species’ first record; the United States’ position on this topic; the Botanical Gardens’ new head gardener; the Seychelles’ tourist attractions.


Some particuliarities of the possessive

Joint possession: Only the second element takes the apostrophe.

Examples: John and Mary’s house; Gilbert and Sullivan’s musicals.

Not joint possession: Belfast’s and Dublin’s transportation systems; John’s and Mary’s cars.