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Here are some items that may help you in your search for a comprehensive history of mail/maille/chainmail:
A Critical Inquiry into Ancient Armour, as it existed in Europe, but particularly in England, from the Norman Conquest to the Reign of King Charles II, by Samuel R. Meyrick (1824). 3 vols.
Worldcat [Link]I’ll point out that a contemporary review of Meyrick’s work was not favorable. You can read it here: [Google Books]
A glossary of the construction, decoration, and use of arms and armor in all countries and in all times: together with some closely related subjects, by George Cameron Stone (1999).
Worldcat [Link]You can see a preview on Google Books – it appears that each entry is rather comprehensive, so this is potentially very good.
Publisher’s Description: Widely considered the classic book in the field, George Cameron Stone’s A Glossary of the Construction, Decoration and Use of Arms and Armor in All Countries and in All Times is an indispensable resource and reference tool for anyone interested in arms and armor. Originally published in 1934, it remains an essential guide to the field. To describe the worldwide range and variety of weaponry, Stone drew upon the more than 4,000 items in his private collection of Eastern arms and armor, as well as the European arms collection of New York’s Metropolitan Museum of Art, and a variety of other sources. Since the author subsequently bequeathed his entire collection to the Metropolitan Museum, this volume serves as an abbreviated visual reference to that institution’s Arms and Armor collection.
By profession a metallurgist, the author focused on techniques of manufacture and workmanship to derive his method of codifying the typology of weapons, relying on an alphabetized dictionary format to avoid the confusions he found in a field without standardized nomenclature. This “glossary” format makes it easy for anyone to locate material on the astonishing variety of weapons covered. These include arquebuses, blunderbusses, flintlocks, wheel locks, matchlocks, and other antique guns; German armor; French rapiers; Roman short swords; Turkish crossbows; all the Japanese bladed weapons (katana, wakizashi, naginata, etc.); the East Asian kris in its countless permutations; and many more.
Illustrated with 875 detailed figures, incorporating thousands of individual photographs and drawings, the book was written from the unique viewpoint of an expert who devoted a lifetime to the field. Hard to locate today (original editions are worth hundreds of dollars), Stone’s Glossary represents a peerless resource for scholars, experts, collectors, students, hobbyists, and institutions — any student of the long history and development of weapons and armor around the world.
British and foreign arms and armour,by Charles Henry Ashdown (1909)
Archive.org (read online): [Link]Wordlcat: [Link]
Hope these help!