Är du färdig med boken?

In English you ask “Have you finished…” using have, but Swedish expresses the result state “finished” with vara + adjective. Here färdig is an adjective, so you pair it with är (the present of att vara) to mean “are you finished.”

Yes, vara färdig med is a common construction meaning “to be finished with” something. You always use the preposition med to link färdig to the object:

• Jag är färdig med arbetet. (I’m finished with the work.)

Both can mean “ready” or “finished,” but:

• färdig focuses on having completed something.
• klar can also mean “clear” or “understood.”
  In many contexts they’re interchangeable:
• Är du klar med maten? or Är du färdig med maten? both mean “Are you done with the meal?”

No, you need med. Swedish uses färdig med to show completion with an object. Without med it sounds ungrammatical—there’s no direct adjective–noun link here.

Swedish yes/no questions use verb–subject inversion. In a statement you’d say:

• Du är färdig med boken.
  For a question, you flip verb and subject:
• Är du färdig med boken?

Using boken (“the book”) indicates you’re talking about a specific book you both know about. If you said en bok it would be “a book” in general, which doesn’t fit most contexts where you ask about a particular text.

Swedish often lets färdig med imply the action is complete. If you need to be explicit you can add att läsa:

• Är du färdig med att läsa boken?
  But it’s usually clear you mean reading.