When can a (spell) skill be levelled?
In the following screenshot I've just gained level 5, and have a skill point to spend:

I want to max Geomancer and Pyrokinetic. Somehow (I do not know how) I achievend 2 points in Geomancer. However, I can not skill up Pyrokenitics. Why?
I've checked around the UI, but there are no tooltips explaining this at all. I've noticed blue stats on my character sheet, but found that these are increases gained from items, which is not the case for Geomancer. I don't understand why Geomancer skill can be 2, but I cannot put my available skill point in Pyrokinetic.
What are the prerequisites for levelling up a (spell) skill?
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Do spells level up in Skyrim?
Yep, you can use the spell 'Muffle' to level up your magic just by walking around. Just cast it and walk around, and it'll increase your level and give you some exp!How do you level up magic in Skyrim?
XP is gained by conjuring. If you aren't in combat, you don't gain as much XP for conjuring anything. In combat, you get more XP the longer your conjured soul lasts and the more damage it does. Once you've conjured a weapon, any damage you do with it gets you XP for the weapon type, but not for Conjuration.How MAGIC LEVEL affects KNIGHTS after adjustments
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Images: Felicity Tai, Felicity Tai, Peggy Anke, Felicity Tai
