Prepositions plus '-ing'

Take a look at the following two sentences - which one is correct and why?

Are you interested in studying English?
Are you interested in study English?

That's right, the first sentence is correct. But why?

When the prepositions in, at, with, of, for, about and so on are used before a verb, the verb must use -ing.

Let's take a look at some other example sentences using prepositions + -ing:

'I'm scared of swimming in the sea.'
'Thanks for giving me a ride.'
'My brothers good at playing tennis.'
'How about taking the bus?'
'I'm not interested in reading books.'

Present Simple and Present Continuous

• She opened the door ___ using a key.
  
  by
  for
  of
  with
  
  
• We have no chance of ___ enough money.
  
  saved
  save
  savings
  saving
  
  
• I am looking forward ___ buying a new car.
  
  to
  on
  with
  by
  
  
• How ___ going for a coffee?
  
  at
  in
  of
  about
  
  
• I'm bored ___ working for my company.
  
  at
  for
  of
  in
  
  
• She was confused ___ trying to follow the lecture.
  
  to
  by
  in
  for