Well depends, where in the 13th century? I guess you mean Europe but even within Europe different areas could field different armies.

A Swedish 13th century army would still be a peasant militia ledung.

The ledung was instituted in the old county laws of Sweden, of which we have the olderst surviving collections and write-downs from the early 13th century, although they may have existed as early as the 11th century.

The earliest source that mentions a Swedish ledung is from 1266, but the administrative division that the ledung is based on, hundare is mentioned on rune stones from the 11th century. Another support for the idea that the ledung existed earlier is the 25-30 runestones raised after men that died in Ingvar den Vittfarne (Ingvar the Far-travelled)'s disastrous viking raid to Russia. Some claim that the vast number and geographical spread of the stones indicate that Ingvar raised a ledung to help brethren Rus vikings against their Slav enemies in Russia in the 1040s.

That said, during the 13th century the ledung was well established in Sweden.

A county was divided into a number of hundare, which was divided further into hamna of 2 villages each. Each village was divided into 4 attungar. Every peasant that owned an attung of land had a duty to go to war for the King if he called the ledung. Peasants that owned less of an attung were grouped together with others until they together had an attung and would draw lots on whom would go in ledung.

The county laws required each landowning peasant to keep and train with arms and have (this varied a bit from county to county, but generally);

• Helmet or iron hat.

• Chainmail or plate (probably refers to coat of plates style armour).

• Spear or long axe.

• Axe or sword.

• Bow with three dozen arrows.

• Food to feed himself for three weeks.

The requirement for arms is heavily debated today - was it an ideal scenario set by the King, or did it reflect reality? It seems like the peasant militia that fell at Korsbetningen 1361 fighting a Danish army of knights and Frisian and German mercenaries mostly wore state of the art coat of plates - but that is later and Gotland was known for being a rich peasant-trader republic that did not pay taxes to anyone.

The ledung would group together in bands of 24 plus one steersman and provide a communally owned ship. Punishment for crimes and fines were much harsher on board than on land.

So, a Swedish ledung army would consist of a King, his personal hird or retuny, some of them maybe mounted, and a large amount of decently well armed, armoured and trained peasant militia that would look a lot like their viking forefathers, use the same tactics and the same formations.

Chicalry was introduced in Sweden in 1280, and there never was more than 400-500 knights in the entire country at any given time, so Swedish knights served as officers rather than as heavy cavalry.