Terrier by Tamora Pierce

Sixteen-year-old Beka Cooper lives far removed from knights, palaces, and the nobility. Her world revolves around thieves, beggars, taverns, and the lowest of the low. She's a trainee for the Provost's Guard—a rookie guard, in a world where a guard makes her own name based on her personality, her attitude toward money, and her love of the law. Beka means to prove that she is out to make her mark in this hard and physical world.

Beka tells her own story in a journal that she keeps from her very first day as a Puppy. The Guards are dubbed "Dogs" in her time and their trainees are called "Puppies." In its pages she writes of her days with her training Dogs, the pair who are to teach her what they know of survival on the streets in the city's toughest slum. Both are veterans. Tunstall is an easygoing, funny man who can be a little crazy in a fight. Goodwin is a small, tough woman who is opposed to Beka's presence at the beginning, a hard Dog and a smart one. They take charge when Beka brings them word of two vicious sets of crimes. Like everyone else in Beka's life, her partners find out that once Beka gets a case in her teeth, she hangs onto it like a terrier until it's been solved.