Dexter season 1 introduces us to a likeable serial killer. We are let into his head to see how he thinks.
Yes, he is a serial killer, and yes, we are meant to like him. First of all, we feel bad for Dexter because something terrible happened when he was three. He watched as his mother was murdered and chopped to pieces with a chain saw.
Dexter's adopted father figured out when Dexter was young that Dexter had urges to kill people. Harry taught Dexter how to kill the "right" people and how to cover his tracks. Dexter follows the code of Harry, which means that Dexter will only kill criminals who were not brought to justice.
Dexter says that he has no feelings. He has learned to fake feelings in order to make it through life with people thinking he's normal. He likes to be alone so that he doesn't have to pretend to feel. As much as Dexter proclaims to not have feelings, he does care very much for his sister, Debra, and for his girlfriend, Rita, and her two children.
He also wishes to have someone in his life who understands him and who he can be himself with. Harry understood Dexter and he's had no one to talk to since Harry's death. He met a kid whom he was going to kill until the kid said that the man he killed had raped him. Dexter let him go, and told him not to kill again, but the kid did. Dexter thought maybe he could teach this kid Harry's code, but before he could, the kid took his own life.
Harry Morgan was at the scene of the crime shortly after Dexter's mother was killed. Harry got Dexter out and then he and his wife adopted Dexter. They also had a biological daughter, Debra. Dexter and Debra remain close, though Debra is frustrated that Dexter never opens up with her. Their parents have both since died.
Dexter hangs out at Rita's quite often. She is the perfect girlfriend for him, because, as he says, she is almost as damaged as he is. She was beaten and raped by her husband and so is content to keep their relationship from becoming physical. Dexter enjoys playing with her two children, Cody and Astor.
By day, Dexter works for the Miami Metro Police department as a forensics expert. By night, he kills and disposes of people who should have been brought to justice but weren't.
Debra works Vice for the same police department until she is promoted to homicide.
Harry had also worked for the police department and is well respected among those who knew him.
The Ice Truck Killer
The Ice Truck Killer kills and chops up hookers, leaving no blood behind. Dexter is intrigued by the precision of this killer's work. He's called the Ice Truck Killer once police figure out he's using an ice truck to keep the bodies cold before he drops them off. It soon becomes clear to Dexter that he's doing this for Dexter.
He leaves Dexter messages, such as a chopped up Barbie doll in his fridge. Dexter loves the mystery and the chase until he connects the killer to Debra. He figures out that Debra's new boyfriend, Rudy, is the Ice Truck Killer.
Dexter follows the clues to a house that he vaguely remembers living in with his mother and big brother, Brian. Rudy is there and Dexter realizes that Rudy is Brian. Brian wants them to be brothers again and asks Dexter to kill Debra, but Dexter kills Brian instead.
This is a turning point for Dexter because he killed the one person who understood him in order to save his foster sister whom he shouldn't have any feelings for at.
Dexter Season 1 - Beyond the Ice Truck Killer
Dexter reports on blood splatter patterns for work and hunts out killers to kill. He hangs out with Rita, but gets concerned when she starts to get physical. Every girlfriend he's had has left him after sex because they saw who he really is, but Rita stayed with him.
Rita's husband gets let out of jail a year early and starts coming around. Rita wishes he would go away and it takes everything in Dexter not to kill him, but he does make it look like Paul is doing drugs, so he goes back to jail.
Dexter helps Debra get ahead in her job, despite the lieutenant, Laguerta, not liking her. Laguerta is replaced when she makes the captain look bad.
Once the Ice Truck Killer is killed by Dexter, and Paul goes back to jail, everything seems to be back to normal with Dexter working with blood splatter by day and killing criminals by night.