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interest2 [transitive]
1 to make someone want to pay attention to something and find out more about it : 
Here's an article which might interest you.
Here's an article which might interest you.2 to give something a lot of attention because you want to find out more about it : He had always interested himself in foreign affairs.
interest yourself in something
formalHe had always interested himself in foreign affairs.3 to try to persuade someone to buy, do, or eat something
Could I interest you in a drink/dessert etc? (=used as a polite way of offering someone a drink etc)
