Kanan Jarrus, born Caleb Dume on Coruscant, is a human Jedi padawan who survived Order 66 at fourteen and spent the next decade and a half pretending he had not. He arrived in 2014 in two places at once: John Jackson Miller's novel A New Dawn (Del Rey, September 2014) and the Star Wars Rebels short "The Machine in the Ghost", ahead of the series itself. Freddie Prinze Jr. voices him.
The name is the character
Caleb Dume was a padawan with a master, a rank and a future. Kanan Jarrus is a name he invented to stay alive. The series is precise about what that costs: he drinks, he lies, he carries a blaster because a lightsaber is a death sentence, and he has spent fifteen years being careful not to be good at the only thing he was ever trained for.
Depa Billaba
Greg Weisman and Pepe Larraz's Kanan — The Last Padawan (Marvel, 2015) is the essential companion text. It puts him in the Clone Wars as Depa Billaba's apprentice, on genuinely warm terms with the clone troopers he commands, and then runs Order 66 from inside his point of view. His master dies buying him seconds. He is fourteen. Everything about the adult is downstream of that page.
Teaching without a licence
What makes him the most interesting Jedi in current canon is that he is unqualified and knows it. He takes Ezra Bridger as an apprentice with no authority to do so, no completed training of his own, and nobody left to ask. He is a half-taught man teaching from memory, and the show treats that as a real problem rather than a plot convenience: Ezra's drift towards the dark side is the direct consequence.
Hera, and a Jedi with a life
His relationship with Hera Syndulla is the other thing canon does with him that Legends rarely did with anyone: a Jedi in a settled, mutual, unglamorous partnership, and the fiction declining to treat it as a fall. Their son, Jacen Syndulla, is born after his death.
The blinding, and the end
Blinded in the second season, he spends the third learning to be a better Jedi without his eyes — the show's most patient writing — and dies in the fourth holding back a fuel explosion long enough for the others to escape. It is one of very few Star Wars deaths that is purely an act of will, with no duel attached.
Where to start
A New Dawn for the man before the show, Kanan — The Last Padawan for the boy, Rebels for everything else. He is canon's answer to the question Legends kept asking: what does a Jedi look like when there is no Jedi Order to belong to?