Along with mounted games and jousting, the IJA has a ground combat component. This is not a re-enactment or choreographed routine, but actual live combat using researched medieval period techniques.
If you are interested in historical ground combat, contact the Academy of European Medieval Martial Arts. These people can train you from beginner through to expert, depending on how much time and energy you want to invest in this art.
The association rules, equipment specifications and certification requirements are set out in the IJA Members Book and the IJA-Canada Members Book, both of which are included with IJA-Canada membership.