Joel is a young man who was not able to complete the all important ceremony that would let him know if he was a rithmatist or not. A rithmatist is able to use chalk to draw figures on the ground to defend or attack other rithmatists. At the beginning of each chapter is one of these shapes with an explanation of the theory behind it. Joel is not a rithmatist but that doesn't stop him from knowing as much about the art as he can. He sneaks into classes and reads everything he can get his hands on. After he becomes friends with Melody, who is a rithmatist, he persuades her to let him into the restricted section of the library for even more in-depth books. They have both been assigned to Professor Fitch for the summer - Melody needs to practice her drawing and Joel needs to assist on a special project tracking down graduates and determining if they are dead, living, or missing.
What is determined is that there have been disturbing disappearances of rithmatics and the two students become instrumental in learning what is going on.
This system of magic lacks the glamour and excitement that readers of Harry Potter are more familiar with. It may take time to appreciate this method of casting charms. We will have to see with the next installment of the series.