's after a noun

[Details]

when do we add 's after a noun?

Is there any difference between "the country's government" and "the country government"? Are both correct?

[Mister Micawber]

This is correct: the country's government.

Use the 's when the meaning is clearly possessive. When the first noun is merely adjectival in nature, do not do so.
_________________
Native English teacher at Mister Micawber's

[Nautilus_001]

so which one is correct, Georgetown University or Georgetown's University? and why?

[Mister Micawber]

Georgetown University. It's the name of it.
_________________
Native English teacher at Mister Micawber's

[HamburgEnglish]

Um ... possesive verses a compound noun?

Compound noun - a collection of nouns to give a better overall meaning

e.g.

Handle
Door handle
Kitchen door handle
Big kitchen door handle
The Country Government

Possesive - belongs to ...

A handle
A door's handle (a handle that belong to a door)
A kitchen's doors' handle (a handle that belongs to a door and the door belongs to the kitchen)
The country's Government (a government that belongs to a country)

.... etc