I don't know of a book specifically targeted ( hah!) at only the history of the arquebus. Osprey Publishing has piles and piles of well-illustrated small books on narrow military topics, and they do have one on pike and shot tactics, as well as on the various armies of the 30 Years War, and the Italian Wars of the previous century: there'd be arquebuses all over the place in them. They are always fun to read, and I'd certainly give one as a present (you could give a new one each year for decades ). And some of them are likely carefully written. But I don't know which...so I would be careful about citing one as a source- I'd try to dig a little deeper if I wanted to do that.

For something more scholarly, James D. Lavin's History of Spanish Firearms has a lot on the development of the arquebus. Not that guns weren't made elsewhere, and Lavin doesn't stop at the 17th c.. But because Charles V found himself enmeshed in constant wars in the early 16th c. he actually funded weapons development, and as the Empire had hard money flowing into it from the New World, he could pay for it. So, a lot of advances happened there- the Spanish seem to be the first ones to have a stringent system for proofing gun barrels, for example. So, Lavin's book is very useful. Lavin was a good scholar ( taught at William and Mary) and delved into a lot of early Spanish sources, so there are plenty of good primary references there. Bert S Hall's Weapons and Warfare in Renaissance Europe is quite good with the advent of gunpowder and gunpowder weapons generally.

More available than Lavin's book is F.A Hayward's The Art of the Gunmaker v. I: 1500-1660 and Torsten Lenk's classic The Flintlock. Hayward deals with lots of pretty pieces, so there's less military . Lenk gets past the matchlock age pretty quick. But if you want to get into details both Hayward and Lenk are good. There are online versions of Lenk, but I would spring for a paper copy, as you really need to have decent photos to catch on to what he's talking about. The original B&W ones in the book were sometimes rough enough, so the scanned photos of them in the online versions are really poor.