The Continental Op is a nameless character and nobody ever has occasion to speak his name: he knows who he is, the reader knows he's the narrator, and he introduces/identifies himself to fellow characters with his business card (people don't tend to read those aloud in real life, so they don't in print either) or the name of his employer. He works for the Continental Detective Agency and has his roots in Hammett's own days as a Pinkerton detective; his cases are all set in the twenties and the violence of Prohibition, bootleggers, gangsters, and labour disputes of that era. Nothing is ever revealed of The Op's personal life either ... he's all about the job when he's working, and that aspect of him is thorough, dedicated, stubborn, and will not leave an assignment unfinished. The cases are always complicated, the characters are complex and unique, and the stories are gripping reads and interesting glimpses into the darker side of the era.
From "The Dain Curse":
Gabrielle's room was empty. Collinson's hat and overcoat were gone; so were the clothes she had taken into the bathroom; and so was the bloody nightgown.
I cursed the pair of them, trying to show no favoritism, but probably concentrating most on Collinson; snapped off the lights; and ran down the front stairs, feeling as violent as I must have looked, battered and torn and bruised, with a red dagger in one hand, a gun in the other. For four flights of down-going I heard nothing, but when I reached the second floor a noise like small thunder was audible below me. Dashing down the remaining flight, I identified it as somebody's knocking on the front door. I hoped the somebody wore a uniform. I went to the door, unlocked it, and pulled it open.
Eric Collinson was there, wild-eyed, white-faced, and frantic.
"Where's Gaby?" he gasped.
"God damn you," I said and hit him in the face with the gun.
He drooped, bending forward, stopped himself with hands on the vestibule's opposite walls, hung there a moment, and slowly pulled himself upright again. Blood leaked from a corner of his mouth.
"Where's Gaby?" he repeated doggedly.
"Where'd you leave her?"
"Here. I was taking her away. She asked me to. She sent me out first to see if anybody was in the street. Then the door closed."
"You're a smart boy," I grumbled. "She tricked you, still trying to save you from that lousy curse. Why in hell couldn't you do what I told you? But come on; we'll have to find her."
There's no particular order to The Continental Op tales other than their chronological order of writing/publication; most of the short stories predate the novels.
The Dain Curse
Short story collections:
The Big Knockover
The Continental Op