Learn German: Ich lese viele Bücher, um mein Wissen zu erweitern. - I read many books in order to expand my knowledge.

It translates to "in order to". The word um comes right after the comma, and zu is placed immediately before the infinitive verb (erweitern) at the very end of the sentence.

Is Wissen in the accusative case here?

Yes. Because it is the thing you are expanding (the direct object), it is in the accusative case. Since Wissen is a neuter noun (das Wissen), the possessive word for "my" stays mein rather than changing to meinen or meine.

Could I use für instead of um ... zu to say "for expanding my knowledge"?

No, German doesn't use für (for) plus a verb to show purpose. Whenever you want to say you are doing something "in order to do" an action, you must use the um ... zu + infinitive structure.

Do I always need a comma before um?

Yes, German punctuation rules require a comma to separate the main clause (Ich lese viele Bücher) from an infinitive clause that starts with um.