Medieval sword fighting has gotten the unfortunate association with LARPing (no, in fact, most medievalists do not LARP), but it was, of course, a serious martial art in the middle ages.
The Academy of European Medieval Martial Arts (AEMMA) in Toronto teaches it like one. Like similar schools across North America and Europe, they have developed a curriculum based on a medieval Italian martial arts manual. Again, this is not the stage fighting you see at Medieval Times, but real, unchoreographed, martial arts training.
They teach broadsword, longsword, and archery, among other things, the weapons you’re trained in depending on your skill level. Check out their website for more information, or try one of the yearly crash-courses they run in collaboration with the ROM (I tried one of these a few years back – it’s a great intro, and a lot of fun! Link to come.)