I've been getting into the Battle Colosseum for the past couple of days and I've noticed that pets have this Spells option... What is this for? How do pets learn spells?

Spells are scrolls. There are many on site, and each requires a certain amount of Alchemy Points (referred to as AP) to equip it to your pet. Your pet gets 1 AP for every 16 intelligence points it has, so if it has 16 intel it'll have 1 AP, 32 will be 2, 1600 it would have 100 AP, and on and on. Scrolls are very useful in battle. They can block, attack, heal, freeze, etc, or a combination of these.

How do you use AP? Do you just equip a spell to a pet?

Yeah, when you click a scroll in your inventory, the next page will have "Teach to (petname)" And then when you go to your pets page and click on a pet's spells, it'll show up there. You can unequip it at any time and teach it to a new pet, or sell it or whatever, but you can only teach it to one pet at a time. The Secluded Shrine is where you make scrolls, although your pet needs to have various amounts of AP to be able to create certain scrolls. Some are also battle loot, or achievement prizes, there are a variety of ways to get them. This thread lists all the scrolls. And this thread is general battle stuff. It has good info on recommended scrolls.

Thank you so much!

You're welcome ^^ Comment me if you have any more questions, battle or otherwise. There's also a battle chat thread that will answer your questions, there are great people over there.

Alright, Thank you ^^