Dead Witch Walking, the Hollows series Book 1 by Kim Harrison
Rachel is a witch employed as a bounty-hunter of supernaturals who commit minor crimes. She impulsively leaves her crappy job to start a detective agency with the enigmatic and scary vampire Ivy. However, her former employer puts a contract out on her life. The only way she can pay it off is to get evidence on the illegal doings of a ruthless tycoon.
Along the way she acquires a magic-using human boyfriend, and negotiates the perils of living with a vampire with a secret agenda. She also learns a lot about pixie clan wars and different types of witchcraft. Written in tough-talking and often hilarious first-person, Rachelís story is a non-stop sequence of funny, klutzy, impulsive, suspenseful, and believable scenes.