The reference grammar English-speaking Danish learners actually keep on the desk.
About this tool →Details
Robin Allan, Philip Holmes and Tom Lundskær-Nielsen cover Danish morphology and syntax systematically with English explanations and plentiful examples, indexed so you can look up a problem rather than read it front to back. Danish is thin on serious reference grammars in English; this is the standard one. It is a reference, not a course — there are no exercises and no audio.