For armour specifically, the best book is still Claude Blair's European Armour c. 1066-1700. It's nearly 70 years old, but it's the only really scholarly general survey done since. Fortunately, it's also a foundational text in armour studies, and mostly holds up - Blair (along with the slightly older generation of scholars like James Mann) was a pioneer in the modern scholarly, systematic study of armour, and he had both a scholarly eye and an incredible breadth of experience in studying, extant armour, documentary records and pictorial depictions. Of course, a lot has happened since Blair wrote, and in particular his primary stylistic division of armour into German and Italian styles (treating other regional styles as minor variations) isn't necessarily tenable, but this is more of a conceptual question than a question of facts. Honestly there's claims in Blair that I didn't understand when I read them that I understand better the more I study the subject.

For both armour and weapons there is Edge and Paddock's coffee table book, Arms and Armour of the Medieval Knight. It's not a scholarly work, but it is a very good general, popular work that has a breadth that's hard to match, and gets most things right.

For swords, Ewart Oakshott's work is very influential and informative (even though I don't always love how sword enthusiasts use it - IE referring to Oakshott's abstracted typology rather than to original swords with all their idiosyncracies). However he was always tinkering with his work, so I don't think I would say any of his works are -introductions-, though Records of the Medieval Sword is a good book with a lot of swords. That said, for a reference book it has issues, since some of the measurements aren't accurate!

Since the history of armour and weapons is considered art history, a lot of the scholarship is done in museums rather than universities, and a lot of the works on the subject are exhibition catalogs or focused studies. If you have access to an academic library I can provide some more scholarly, harder to find titles.