I'm not particularly familiar with Danish books of this period, but I have worked with (and own) several English books of similar date.

I obviously can't give a cast-iron guarantee that the book is original, but I don't see anything inconsistent with it dating from 1688. The style of binding was certainly in use at that time, and I have seen several books from the period with similarly good print quality.

If it was a later edition then one would expect the date on the title page to reflect that (if it was English, anyway), so I don't think that it is. This leaves two possibilities, either it's genuine and dates to 1688 or it's a modern forgery.

I might be wrong, but judging from the picture and the wide margine it seems to be one of the books published by Joachim Schmedtgen, who printed them in 1683.

Here is a link to another of his books: http://www.lynge.com/item.php?bookid=1177

I apologise for any grammar/spelling mistakes. English is not my native language.

No need to apologize. Your English is about 350% better than the vast majority of reddit anyway. Congratulations on the find, and I hope you can have it authenticated or at least appraised. There's what I think is a copy of the same book you have on AbeBooks for about $1800, but I can't be sure because the description isn't in English. Hope it helps anyway and best of luck to you.

Here are pictures of Kong Christian Den Femtis Danske Lov, 1683, from an online auction site.

As you can see it's identical to yours. Even down to the handwritten legal notes on some of the pages. It's not really very valuable (for a book of that age), since it was printed in rather large numbers and those with a copy kept them around. Still a very cool thing to find though, obviously!

I have to say this is exciting. Where did you find it? Have you read a bit in it? What's it about?

Have you tried taking it to you professor or teacher at your university? Or maybe emailed them? Maybe they could give some insight on the book. Since you are danish I know that the last year ph.d. from Aalborg University wrote his paper about english seafarers in 1577-1744, but also taught a course about danish naval history in the same time frame. Maybe he can give some insight, if this proves fruitless and you stay eager about it.