This is the result of a project by the British Natural History Museum to catalog the entire fauna of the Hawaiian Islands. It took over 20 years from start to finish, and although it obviously came nowhere near its goal (one only need look at the number of species described in the Insects of Hawaii series to see that), it is the foundation on which all the later works were built. It was primarily driven by David Sharp, the overall editor and organizer, and Robert Cyril Layton Perkins, who did much of the collections.
It was published in 18 sections between 1899 and 1913, which were later bound into three volumes. Unfortunately, like many books of that period, it was printed on acid-bleached paper (ironically, books from the 1600's are often in better shape than those from the early 1900's). As a result, the books are now extremely fragile, and most libraries will not allow you to make copies of it – never mind the fact that you're dealing with a hundred-year-old, 600-page book.
Fortunately, I obtained a photocopy thanks to David Foote and Pete Oboyski, and scanned it to pdf (thanks also to Curtis Ewing for scanning the figures). It is now complete; previously, issue 1.6 (Introduction) was missing pp. ccxxiv-ccxxv, and issue 3.1 (Diptera) was missing pp. 34-35, so if you downloaded it before June 2007 you should get the new versions of these sections. The links are below, broken up by sections. Some issues contained more than one section. The illustrations are included with the section they go with; you can also download all the illustrations in one file. It is also important to note that they were not bound into volumes in the order they were printed; for example, the Introduction is in volume 1 even though it was published last. Also, the filenames have spaces in them, so to save them, right-click and use "Save Link As" instead of saving from the Acrobat reader, which will give you "%20" instead of the spaces.