Terrier, by Tamora Pierce, 2006. Beka Cooper Book 1.
"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 cop, in a world where a cop makes her own name based on her personality, her attitude toward money, and her love of the law".--Tamora Pierce
Bloodhound, by Tamora Pierce, 2009. Beka Cooper Book 2.
"Beka is finally a Dog—a full-fledged member of the Provost’s Guard, dedicated to keeping peace in Corus’s streets. But there’s unrest in Tortall’s capital. Counterfeit coins are turning up in shops all over the city, and merchants are raising prices to cover their losses. In Port Caynn, Beka delves deep into the gambling world".--publisher's description
Mastiff, by Tamora Pierce, 2011. Beka Cooper Book 3.
"... a tasty blend of detective work, romance, magic, and treachery. A king's son has been kidnapped and Lord Gershom calls in the best team he has: Beka Cooper; her canine tracker, Achoo; Beka's partner Tunstall and his Lady Sabine; and a seemingly bumbling mage known as Farmer Cape".--Cindy Welch, Copyright 2010 Booklist
Tamora Pierce's series are listed below in the chronological order in which they take place. My advice is to start with Alanna and proceed from there. Click on the series title to go to the Library's online catalog:
The Song of the Lioness (4 in series)
The Immortals (4 in series)
The Circle of Magic (4 in series)
The Protector of the Small (4 in series)
The Circle Opens (4 in series)
The Will of the Empress
Trickster (2 in series)
Beka Cooper (3 in series)
Tamora Pierce website