Brandon initially planned to use the phrase "Ars Magica" for these glossaries, as he felt it was "a cool Latinate take on 'Magical Arts' or 'Magical Skills'." However, there was a role-playing game with that name, so he instead went with "Ars Arcanum," which he ultimately felt had more of a true-Latinate feel.
Ars Arcanum in each book or series
All of the cosmere stories containing an Ars Arcanum are listed here in rough chronological order.
Elantris has an Ars Arcanum that lists selected Aons of note and includes their design, their meanings, and some examples of their use within Aonic names or terms. The tenth anniversary edition added a brief essay titled "On AonDor". The essay raises questions about the origin of Aons and compares the manifestations of Investiture found on Sel to those found on other planets. Selish magic is noted to have several unique qualities that Khriss cannot explain. The essay is also notable for mentioning Vax.
The books in the Mistborn series each have an Ars Arcanum with the table of Metallic Arts, describing what each of the Allomantic metals does. Since more metals are discovered and new things about them are learned, the table in each later book has more metals and information with greater accuracy.
The Stormlight Archive
The Ars Arcanum in The Stormlight Archive gives detailed information about the Ten Essences, as well as descriptions of the different Surges and how they are used by Surgebinders. Some information has been added in each book: a Lightweaving section appears in Words of Radiance and Oathbringer contains an additional section about Soulcasting. Rhythm of War contains an additional section about the Surge of Cohesion, particularly focusing on its use in shaping stone.