Any suggestions for books that thoroughly talk about medieval armor during the middle ages?
This is a good question! We have some recommendations in the booklist. I'll just copy them here and expand on them a bit plus add a few.
Blair, Claude European armour, circa 1066 to circa 1700 London: Batsford, 1958. The best overview of European armour from 1066-1700, with a particular emphasis on the development of plate armour. It is primarily a descriptive history of armour's form. Though it is 60 years old, it's still the standard general history on the topic, and hasn't been surpassed. This book should be available via interlibrary loan from a public library or academic library or on the shelves in many academic libraries.
Williams, Alan The knight and the blast furnace : a history of the metallurgy of armour in the Middle Ages & the early modern period Leiden ; Boston : Brill, 2003. A detailed metallurgical analysis of hundreds of surviving pieces of plate armour. It also includes historical sketches of the armour industry in different cities, accounts of medieval and early modern steelmaking and a final chapter evaluating the effectiveness of armour. This is hard to get ahold of - my copy was $350 and one of the best purchases I ever made. For getting a loaned copy you'll need academic library access or to go in person to some place like the US Library of Congress.
Pfaffenbichler, Matthias - Armourers - this is a great one-volume overview of the armour industry. Not much about the armour itself, but a lot about the people who made it.
Edge and Paddock, Arms and Armour of the Medieval Knight - not as thorough as Blair, but easier to get ahold of and with more pictures, this is another decent intro to armour. It's organized in a way that's a bit maddening for reference, but there's a lot of information here.
LaRocca, Donald How to Read European Armour - this is a different sort of introduction, that gives you an introduction to armour as an object and gives you a guide to looking at it critically in settings like Museums. Includes a lot of great information about what armour -is-, though it isn't really a history of armour per se.