I wouldn't use "on" in that sentence, Richard Andre Herrera. I'd use "of". However, I have heard and read others use "on" after "knowledge". It means the same thing as "about".I wrote a review in Amazon.com about a book, more or less the following: "Anyone who wants to deepen his/her knowledge on Latin American literature." Is it ok?
Actually, Egmont, quite a few native speakers do use the preposition. Looking through COCA* for "knowledge on", I found 311 examples with that combination. Not all of them apply to what we're discussing here, but these do. All examples here come from edited publications:"Knowledge of Latin-American literature" is what I, and I believe most native speakers, would usually say or write.
"Knowledge about ..." is also correct, but less common even though the usage "to know about something" is standard. You could write "Anyone who wants to know more about Latin-American literature ..." if you wanted to. That also avoids the problem of gender-specific pronouns.
"Knowledge on ..." is an error. One does not "know on" something in English.