These are adjective + preposition form. Many adjectives are used in this form. One must know which prep follows which adj.
Someone is 'interested in something' like,
Mr. X is interested in reading books.
Interested is adjective. It means 'showing interest' and the preposition in will follow. Who is showing interest? Mr. X. So the adjective interested is describing whom? the noun - Mr. X.
fond is another adj; it takes the prep 'of'.
'fond of' means - strong liking
mad about is another adj, it takes the prep 'about'
i am mad about my son
be mad about sb/sth to love someone or something.
There are many more such adjective+prep - one just has to know the meaning of the adj and be sure which prep to follow and use.
like: good at, careful of, passion for etc.
But, sorry I don't know the use of keen on! If keen means 'strong' then what I know is we use it before noun, like: keen interest, keen sense and so on!
- For Teachers