Since the chapters alternate between Sadima's perspective and Hahp's perspective, we're gonna lump each character's plot highlights in together.
Sadima's mom dies giving birth to her—oh, and because a magician that Sadima's brother, Micah, hired to help with the birth turns out to be a fraud. Sadima grows up with Micah and their dad on the farm, but Sadima realizes that she's different from them because she's always been able to hear the thoughts of animals. When she's fourteen or so, Sadima meets a young man named Franklin, who says he wants to work to restore magic in the world. He thinks her link with animals could be helpful with this, and he says to come find him in the city of Limòri if she's interested.
Sadima's dad dies a few years later, and her brother's going to marry this chick he's into. Sadima decides to go find Franklin in Limòri. There, she lives with him and Somiss, who seems to be in charge. Sadima cooks and cleans for them, and she also makes copies of Somiss's research notes for him (she can't read when she starts, but she eventually teaches herself to). Things begin to get weird when Somiss goes on this power trip and becomes paranoid about his dad being on his tail to make him stop researching magic.
Sadima wants to leave this clearly abusive situation, but she's fallen in love with Franklin and she can't leave without him. Someone sets their home on fire, and the three escape into the night, heading for some caves that Somiss thinks are the ancient home of magic.
Hahp is 11 when his dad (who seems like a huge jerk) takes him to the school of magic and basically just leaves him there. There are nine other boys, and the wizards tell them that only one will survive the training. Hahp gets stuck with the only boy who's a commoner, Gerrard. At first they're starved and not allowed to sleep—and then the psychological torture begins. The leader of the school, Somiss (that sounds familiar…) starts turning them against each other, and their main teacher, Franklin (that sounds familiar too…) begins to teach them to control their breathing and calm their thoughts in the midst of all this craziness.
Hahp passes the first few tests, such as learning to magically make food for himself so that he doesn't starve to death, and he also learns to move his thoughts into animals (thus saving him from a deadly snakebite—also a test, woohoo). Despite being repeatedly told not to help the other students though, Hahp throws Gerrard a lifeline. They eventually decide to secretly cooperate so that they can both survive the training and get revenge on the wizards who are killing boys as part of their training process.
What do these two plotlines have to do with each other? By the end of Sadima's story, we learn that Somiss wants to start an academy for magic. And that academy is exactly where Hahp ends up. How long has passed between their two storylines, and what happens to Sadima, Franklin, and Somiss in between the two timelines, though—that's a mystery.