I've just reached chapter three and went on my first adventure in Campana. I've gotten two or three badges there. What are they for? (Can't find them in the inventory)

Badges are for combining monsters. you can give the baby one badge and the'll learn the trait off the start.

And if you want to see a list of what you have,they're in the "combined" list in consumable part of your items. It's a long list and IIRC the first ones I got were way at the bottom, so you may have to scroll down a lot to see them at first.

Don't forget that some badges are species specific Like giving a tiger monster a Dragon badge won't get it to learn the trait from that badge.