Learn Finnish: Opiskelijalla ei ole kirjaa. - The student doesn't have a book.

Finnish does not have a direct verb for 'to have'. Instead, you add the ending -lla or -llä to the owner and use a form of the verb olla (to be). The literal structure of this sentence is 'On the student is not a book.'

Why is the verb ole instead of the usual on?

In negative sentences, Finnish uses the negative word ei combined with a special stripped-down form of the main verb. For the verb olla, this form is ole. Together, ei ole means 'is not' (or in this structure, 'does not have').

Why does kirja have an extra -a at the end to make it kirjaa?

This is the partitive case. In negative 'have' sentences, the thing that is not owned must always be in the partitive form. Because the student does not have the book, kirja takes an extra -a to become kirjaa.

If I wanted to say the student does have a book, would I just say Opiskelijalla on kirjaa?

Not quite! In a positive sentence, a single, countable object like a book stays in its basic form. So 'The student has a book' is Opiskelijalla on kirja. The partitive form kirjaa is only triggered here because the sentence is negative.