In the 6th main world, called Celestia, there is astral magic. You can't choose any of the astral schools as a primary school, but you want to save training points to learn astral magic.
The three types of astral magic:
The Sun School : Enhances other cards in your deck, in ways such as increasing damage, like permanent trainable versions of the tough treasure card, except you get enchantments with more damage later on. There is also accuracy enhancers, but usually gear itself can cover accuracy needs.
The Moon School: Used to transform into creatures of certain classes, and gives you a new deck with new spells to use depending on which creature you are polymorphing into. Most people just skip out on the Moon School, as it is easier to just focus on your main school.
The Star School: Has auras over you for a couple of rounds, and gives certain effects depending on the card you are using. For example, the Amplify spell gives you +15% damage to any spell for four rounds, and then the aura wears off. There are plenty of other star spells you want to look into, also.
In the 10th main world, you are introduced to shadow magic . When you learn it, you will gain a new pip type called shadow pips. Shadow spells will cost 0 normal/power pips, but will cost 1 or 2 shadow pips instead. Shadow spells vary in effects, as some are similar to star spells, in which you get enhancements for a few rounds, but others just do damage on their own. You get 1 free shadow spell depending on your school though, so I don't think you need to invest that much into shadow spells, but you will know if they are worth it or not by then.
In Celestia (around level 50), you gain access to the Astral Schools which include Sun, Star, and Moon. These aren't self-sustaining, but they help you along with your main schools. They have spells all throughout the second and third arc.
In Khrysalis (around level 90/100), you gain access to Shadow Magic which acts a little like Death in the fact that it helps you, but also hurts you.
In Darkmoor, you gain Shadow-enhanced spells like Glow Bugs or Call of Khrulhu that need a certain amount of regular pips and a shadow pip.
Kingsisle should be adding some more new schools as well.