A. If a preposition (in/for/about etc.) is followed by a verb, the verb ends in ~ing.
For example:
Are you interested in working for us?
I'm not very good at learning languages.
She must be fed up with studying.
What are the advantages of having a car?
This knife is only for cutting bread.
How about playing tennis tomorrow?
I bought a new bicycle instead of going away on holiday.
Carol went to work in spite of feeling ill.
You can also say 'interested in somebody (do)ing .....', fed up with you (do)ing...' etc.:
* I'm fed up with you telling me what to do.
B. Note the use of the following prepositions + ~ing:
before ~ing and after ~ing:
Examples:
Before going out, I phoned Sarah. (not 'Before to go out')
What did you do after leaving school?
You can also say 'Before I went out ...' and '... after you left school'.
by ~ing (to say bow something happens):
Example:
The burglars got into the house by breaking a window and climbing in.
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She made herself ill by not eating properly.
without ~ing:
I ran ten kilometer without stopping.
They climbed through the window without anybody seeing them. (or ... without being seen.)
She needs to work without people disturbing her. (or ... without being disturbed.)
It's nice to go on holiday without having to worry about money.
C. To ~ing
To is often part of the infinitive (to do/to see etc.):
We decided to go out.
Would you like to play tennis?
But to is also a preposition (like in/for/about/from etc.). For example:
We drove from London to Edinburgh.
I prefer tea to coffee.
Are you looking forward to the weekend?
If a preposition is followed by a verb, the verb ends in ~ing; (in doing/about going
etc. So, when to is a preposition and it is followed by a verb, you must say to ~ing:
I prefer driving to travelling by train. (not 'to travel')
Are you looking forward to seeing Ann again? (not 'looking forward to see')