Grammar

A Concise Contrastive Grammar of English for Danish Students

L. Hjulmand & H. Schwarz, Samfundslitteratur, 2008, second edition.
An excellent book for clearing up difficulties with going from Danish to English writing. Very comprehensive and detailed explanations and examples comparing Danish to English, including several sections on ‘Problems for Danes'. 

Advanced Grammar in Use

M. Hewings, Cambridge University Press, 2005, second edition.
Quite a high level grammar explanation/exercise book, it is useful for very fine differences between various grammatical structures. It also includes a very good unit on ‘Linking words'.

English Grammar in Use

R. Murphy, Cambridge University Press, 2004.
The most popular of the ‘Grammar in use' series. Very practical as both a grammar reference and self-study book. Each unit consists of just one page of explanation and an accompanying page of exercises, making it very user-friendly. 

Essential Grammar in Use

R. Murphy, Cambridge University Press, 2007, third edition.
The more basic grammar level version of English Grammar in Use. 

Fejlstøvsugeren: Grammatisk øvebog i engelsk

J. Bøgh & J. Hovgaard, Musagetes, 1987.
Bit old perhaps now, shown by some of the rather unnatural examples, but it has a good, concise section on commas and has the advantage for Danish students of being in Danish.

Grammar Scan - Diagnostic tests for Practical English Usage

M. Swan & D. Baker, Oxford University Press, 2008, third edition.
A graded series of exercises for self-study and to use together with the book ‘Practical English Usage' (see section B above).