As your Hero levels up and gets stronger, so too can your Spells.
This can be done by navigating to the Gear Screen, tapping on the Spell book under your Hero and then selecting the Spell you want to upgrade.
A Spell that can be upgraded, is indicated by a green Upgrade button. If this is greyed out, then you are missing some of the components to upgrade this spell at the moment.
This will display your current max level available for upgrading. You can select a lower level to upgrade to before confirming your Upgrade.
Note: If you equip a Spell with a higher level than your Hero's level, the Spell will only have the effects as if it were the same level as your Hero.
If the Dark Firebolt Spell is level 25 and you equip it to your level 1 Hero, then a yellow down arrow will appear next to the Spell's level and effects and it will display as a level 1 Spell when you view it on your level 1 Hero.
Upgrading Spell Rarity
After you have upgraded your Spell to Level 5, you can then increase their Rarity.
Once a Spell reaches Level 5, it will increase in rarity after every 10 levels. The highest level is Mythic, after your Spell is over level 45.
With each level a Spell is upgraded will grant it an increase to the amount of damage dealt and with each Rarity an increase to it's ability.
Example: If I upgrade Witchbolt to Epic, it will get an extra 10% chance to regain half mana, but once I level it to level 26 I will get an increase to the damage it deals.