You cannot level up your spells per se, they get better if you build shrines on elemental shards you find on the map (fire, earth, water, air, life, death). When a champion reaches the next level you can spend one trait point in the general or class specific tree. Elemental, Life and Death spells are in the general tree, but your champions must have the proficiency for it to get these spells. Sovereigns can steal a spell proficiency they lack from another champion, but that champion is sacrificed in the process. You can also pick a faction with "The Decalon" trait and buy elemental spellbooks in your shop after you have researched a specific technology in the Magic tree or buy the books in the shop of an enemy AI if they have that faction trait and you are on good terms with them. Champions must have reached a certain level before you can unlock the next spell tier. (hover over the next tier). Other spells can be unlocked as a mage in the class specific mage tree and if you research certain technologies in the Magic research tree.