A. Prepositions can have meanings other than place or time. Here are some examples.
We were arguing about politics.
According to the opinion polls, the government is very popular.
The resort was very crowded. And as for the accommodation, it was awful.
We need some advice as to what we should do next.
I'm reading a book by Thomas Keneally.
Contrary to popular belief, prisons are not holiday camps.
The couple want to stay together for the sake of the children.
On behalf of the company, I would like to express my thanks.
No action has been taken regarding / with regard to my complaint.
B. For has a number of different meanings. Here are some of them.
Could you do something for me, please? (= to help me)
I've called in for a chat. (purpose)
She's a very clever girl for her age. (= considering her age)
Are people for the scheme or against it? (= in favor of/supporting)
When for means 'in favor of', it is normally stressed.
C. With has these meanings.
I went to the concert with a friend. (We were together.)
Matthew is the man with long hair. (He has long hair.)
I cut the wood with an electric saw. (I used an electric saw.)
We all set to work with enthusiasm. (= enthusiastically)
With people watching I felt embarrassed. (= Because people were watching...)
Without is the opposite of with.
Who's the man without any shoes on?
We all set to work, but without enthusiasm.
NOTE:
We can use with + noun to form an adverbial expressing manner or feeling.
I listened to the discussion with interest.
With certain nouns we use in.
The losers sank to the ground in despair.
D. Of has a number of different meanings.
a tin of soup
the end of the game
some of my friends
our first sight of land
We can also use of in this pattern.
These souvenirs are of no value. (They have no value.)
She's an actress of great ability. (She has a great ability)