Aslan famously roars at the Ice Queen “Do not cite the Deep Magic to me, Witch! I was there when it was written.”
So who wrote them? Was there a negotiation process? Since some Deep Magic favours the Witch and can even bind Aslan. Is there a full list? Why are there in place to begin with?
The Emperor-beyond-the-Sea wrote the deep magic. There was no negotiation, as He rules everything, not just Narnia, but every world. The magic doesn't favor anyone, it simply is. His motives for putting it into place are inscrutable, unknowable for people like us. Which is kind of the point. The shattering of the stone table represents a breakdown of everything that Narnia was, all that old magic and laws and everything being literally set in stone. Aslan's resurrection, shattering the stone, was immediately followed by a joyous romp. This heralds the new Narnia: Freedom, happiness, and life. You could say that the deep magic was written purely to lead to that moment.
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Also notable: We literally see the world of Narnia being brought into existence by Aslan in The Magician's Nephew, without a mention of any Deep Magic, implying that the Magic was written before Narnia itself existed. This is corroborated by the fact that there is Deep Magic from the Dawn of Time, and Deeper Magic from Before the Dawn of Time.
The only rules of the Magic that we know of is that Jadis is entitled to kill any traitor (the Deep Magic), regardless of circumstances. This represents Jadis's position as the Satan of Narnia. The apocalypse would occur if she were denied her right. However, the Deeper Magic states that if she claims a traitor, then instead punishes an innocent in the traitor's place, then the Stone Table (where the Deep Magic is written) would crack, and Death itself would work backwards, restoring the innocent to life.
Aslan is aware that Jadis (the White Witch's real name) was not present before the Dawn of Time (having arrived only when the world had already begun to be made in The Magician's Nephew) and thus didn't know about the Deeper Magic. He offers himself in Edmund's place to be punished, and is restored to life. Since in Lewis's work, the Emperor is the same figure as the Abrahamic God, the Emperor is once again teaching the world His message: Aslan is Jesus, as Jadis is Satan. This is meant to represent the story of Moses and the Commandments (the Stone Table), Jesus's temptation (Susan offering to help Aslan work against his fate), Jesus's resurrection (Death working backwards for Aslan), the New Covenant (Narnia without the Stone Table), and Saul's redemption (Edmund becoming a just leader).