What is the difference between 'keen on' and 'keen to'?

Keen to + base form of verb. The "to" + verb is the infinitive form.
Keen on + present participle: This is the gerund form. "on" is a preposition.

There are instances where you have the choice of a gerund or infinitive.

Thanks for the reply.

There are instances where you have the choice of a gerund or infinitive.

Could you please give me some examples?

I love looking at art.
I love to look at art.

I prefer to study by myself.
I prefer studying by myself.

I have started working on my project.
I have started to work on my project.

These have different meanings:

I regret to tell you that you weren't invited.
I regret telling you that you weren't invited.

I forgot locking the door.
I

Thanks for the help. Does the sentence 'I forgot locking the door' mean that you did the action(of locking the door) but you don't remember the action? But in second it means that the doer didn't do the action at all, right?

fatimah0786Thanks for the help. Does the sentence 'I forgot locking the door' mean that you did the action(of locking the door) but you don't remember the action? But in second it means that the doer didn't do the action at all, right?

Correct. They are almost opposite in meaning.

I would say that 'keen to' is more commonly used for a specific, current action, e.g. I am keen to get started on this project; whereas 'keen on' is more commonly used to express a general preference, e.g. "I'm not keen on sprouts". It would sound strange to exchange the two sentences here as one is very clearly talking about a present situation and one is clearly about a general preference. T