Which Hiram Maxim? The father (inventor of the machine gun) or the son (inventor of the automobile muffler and the firearm sound suppressor, which are pretty much the same thing aside from what they are attached to)?

I don't know of any good biographies, but a good introductory book for bigger-picture stuff is The Gun by C. J. Chivers, which covers the history of the Kalashikov rifle. It goes over the technological developments leading up to it and spends some time on Maxim. Keep in mind, though, that since Chivers is a journalist, rather than an academic, it's probably best to use that as an introduction, rather than your main thing.

Hiram senior is featured in The Social History of the Machine Gun by John Ellis, a classic little book and great fun to read as well. It is perhaps a trifle dated: I think it can be faulted for buying into the idea that the generals in WWI were all stupid donkeys, had no notion of change, innovation- a view which has been modified in the past 30 years since Ellis' book.