It would definitely be better to wait for the answer from specialists of this field, but I can definitely recommend Marcus Rediker's Villains of All Nations: Atlantic Pirates in the Golden Age, Boston: Beacon P, 2004 as an introduction to the topic. Though short and after 1720s is not dealt throughly with the book, it includes some interesting chapters like the social as well as geograhical origins of the pirates, and how they kept 'their order' on shipboard.

My acquaintance who writes the relationship between the piracy and Britain also makes use of David Cordingly, Under the Black Flag: The Romance and the Reality of Life among the Pirates, New York, 1996 and D. Cordingly (ed.), Pirates: Terror on the High Seas, Atlanta, GA, 1996, though I don't recommend the latter for the handbook for the Vikings as well as non-European pirates.

[Added]: It would also be useful for the better understanding in the 'twilight of Piracy' during the 1720s to distinguish the 'unlawful' piracy and the privateering under the approval of the states, and to pay attention to the fact that the legal concept of the latter was formulated at that time (David J. Starkey, British Privateering Enterprise in the Eighteenth Century, Exeter, 1990).

[Edited]: fixes typo mistakes.