Making an Adept III spell is no different to making a chair or a backpack. Just follow the recipe.
The problem comes in the ingredients which are rare.
You have to make a reagent (from Lapis or Copper for Tier I and Coral or Silver in Tier 2) to make the dye to make the ink. The recipes are in Artisan Refining 4 or Advanced Scholar Refining 11.
After that it's just like making anything.
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Wherever I go - there I am.