Exploring dungeons you may found a book at the end of it, if you interact with that you learn a new magic.
For what a know, there is healing in the slime cave, fire bolt in the goblin cave and summon skeleton warrior in the big tower on the north of de main city
right in the entrace of the main city there is a guard in front of a house with a sword simble, you just need to suck him off or pay 100g then you can train with the captain of the guar, aftar a little bit of training you become a swordsman and can use a sword