The Middle Ages or Medieval Period covers quite a large amount of history. Beginning in the 5th century, it spans all the way into the 15th century. Naturally, such a long period of time allows for numerous changes in weaponry. While we can't cover all of them in a single sitting, here are some common types of medieval swords.
The Classic Medieval Sword
While the name may not conjure images of greatness, it is apt. When people tend to visualize the most bare-bones version of a sword, this is probably what pops into their head. A cruciform sword, this means that the hilt extended from the sides enough to form a cross or lower case "t" when observed. Double edged and meant for one-handed use.
The War Sword
In the Early Middle Ages, this was the "go to" sword. While its name is somewhat of a catch-all title for swords used in war, it was also known as an Arming Sword. This makes it easier to define as a double-edged, cruciform sword that was widely used in military combat. Light enough to be used with one hand, this sword made a great pairing with shield or buckler.
Typically single-edged, the Falchion
had incredible utilitarian chopping power but was versatile enough for close quarters combat. Few original pieces have survived the years and because of this, placing the sword among classes has been difficult. Useful outside of battle, it seems likely that this sword would be common among the lower classes. But the sword is frequently depicted among archers and mounted knights as well.