The main character of the novel. The son of a cleaning lady and a chalkmaker, Joel is neither the scion of powerful or influential people nor, to his great regret, a Rithmatist. He attends Armedius academy due to a scholarship granted to him by Principal York after his father's death eight years previous to the beginning of the book.
Belligerent Sexual Tension: A schoolboy variety, with Melody. He comments several times during the book that she would be quite pretty - if she weren't so annoying.
Brilliant, but Lazy: He's quite bright, and is in fact something of a savant when it comes to math and Rithmatic theory, but his obsession with Rithmatics leads him to neglect other coursework - he's failed at least one course every semester since he started at the Academy.
Disappeared Dad: Died 8 years ago after a railroad accident. Apparently, at least. Joel's mother let slip that this might not have been an accident.
I Just Want to Be Special: Obsesses over Rithmatic theory, partially due to his own father's interest in the subject. His biggest regret is that he can't actually use what he knows - he has no true Rithmatic ability.
Missed the Call: Joel could have been a Rithmatist, but something happened to keep the process from happening properly… both times.
Melody and Joel in the book trailer.
A red-haired Rithmatist the same age as Joel. While she's an excellent artist (and thus exceptional at using Lines of Making to summon Chalklings), she's VERY poor at the geometric aspects of Rithmatics - so poor, in fact, that she winds up in a remidial course with Professor Fitch over the summer.
Drama Queen: The fact that we have to list this trope is tragic!
Girly Girl: Her defensive chalklings are unicorns, which she doodles alongside castles instead of taking notes, describing them as an "elegant and noble creature" whenever Joel speaks against them. She also mentions wanting to use pink chalk.
Also inferred, Word of God explaining that "in The Rithmatist, one of the things [he] wanted to do was write a female character who is more girly, so to speak. [He] wanted to make her a strong protagonist in a way that does not undermine her femininity."
I Just Want to Be Normal: Melody resents her Rithmatic powers, which she never asked for, because it means she's essentially been conscripted to train to fight the Wild Chalklings, and she doesn't actually have much skill at drawing defenses or strategizing. In this, she acts as a perfect Foil for Joel:
Tsundere: Again, seems to be going here with Joel.
The Unfavourite: Not explicitly stated, but strongly implied, due to her lack of skill compared to her older siblings.
One of Armedius Academy's foremost Rithmatics professors. A scholar, teacher, and historian rather than a warrior, Fitch doesn't have the nerves to be much of a combatant, but he's a brilliant theorist.
Dual Wielding: The climax has Fitch with a piece of chalk in each hand. It's more badass than it sounds.
The Obi-Wan: Older? Check. Teaches the protagonist? Check. Not the hero? Check (mostly, see above).
Professor Andrew Nalizar
An ambitious new Rithmatics professor. Tall, handsome, and arrogant, he tends to rub almost everybody the wrong way - especially Joel, who immediately suspects him when unusual events start taking place.
Affably Evil: When Joel realizes he was the mastermind behind the Scribbler plot, he drops the Jerkass Façade, calmly admits it (while noting Joel won't be able to prove it, and would look like an idiot trying), explains a few other minor plot points, and even apologizes to Joel for repeatedly failing to recognize him.
Nalezar:I have trouble telling the difference between those of you who are not Rithmatists, you see. You all look so alike.
The Chessmaster: Arranged for the entire plot of the first book to happen in order to gain trust and authority at Armedius, thereby putting himself in charge of the training of the next generation of Rithmatists to be shipped out to Nebrask.
Expy: of Professor Snape. Arrogant, cruel, very powerful at his magic, always suspiciously seeming to be involved in the bad things going on, and yet held to be above suspicion by the authority figures. In the climax, Joel catches him red-handed, mixed up deeply in the attack on the school, and douses him with chalk-destroying acid, only to find that the real bad guy is the federal investigator, and Nalizar was trying to fight him off! Climactic chalk-battles ensue, and in the end, he's defeated, and Joel has to admit that Nalizar really was a hero and a good guy afterall... only to discover, a few days later, that there were two villains, and Nalizar helped take down his compatriot so as to establish himself as above suspicion in the very organization that is training the people who will be fighting the bad guys!
One of the clerks in Armedius's office building. A friend of Joel's mother and a bit of a gossip, which makes her a useful, if somewhat hazardous source of information.
Vitriolic Best Buds: With Exton - she treats him like a humorless fuddy-duddy and delights in distracting and annoying him, but is one of his foremost advocates when he's accused of being the Scribbler.
The other clerk in the Armedius office. Portly, mostly humorless, but secretly fond of Joel and Florence.
Red Herring: He's actually 100% innocent of the crimes.
Vitriolic Best Buds: With Florence - He constantly complains about her interruptions and annoyances, but is glad to see her once he's released from prison.
Principal Thomas York
The head of Armedius Academy, York is a brilliant administrator and a kindly man. He is friends with Professor Fitch and was once friends with Joel's father, and thus is somewhat softer with both than another administrator might be.
Reasonable Authority Figure: Played refreshingly straight. York manages to juggle the egos of the powerful students and parents at his school and still keep the place running well.