Summary may contain SPOILERS

Quick Read:
Episode 01 of Elfen Lied focuses on Lucy violently escaping the facility where she is held, then meeting up with two college students named Kouta and Yuka. After coming across Lucy, the pair decide to take her to the Maple Inn, which is where Kouta is staying while he's going to school. They conclude that she doesn't speak their language, because the only thing she's said to them so far is "Nyu", which becomes her name. It is also pointed out that something involving both Lucy and Kouta occurred in the past, but Kouta doesn't remember it right away. He does however, remember his dead sister which makes him show Nyu and Yuka a sea shell she collected for him when they were little. Nyu, seeing how sad the shell is making Kouta, breaks the shell in half, hoping to spare Kouta the bad memories. Turns out that wasn't the best move, Kouta harshly yells at Nyu, making her run crying into the night, to the beach where she was first found. End of episode. (Vyrik)

Summary:
It is in this episode where Lucy escapes the confines of her prison, and stumbles upon our young hero, Kouta. The episode begins showing Lucy bound and suspended in some kind of prison chamber, with a few fear stricken guards around her. This is where it all begins, she kills one of the guards and takes the key to her prison, letting herself out using her vectors. For those not familiar with the anime, "vectors" are kind of like telekinesis, they're invisible arms that can manipulate objects, Lucy has 4 of these, each with a reach of 2 meters (6.56 feet). Now the fun starts, she quickly finishes off those remaining in the room and leaves her cell twisted and completely disfigured. More guards are alerted to her messy escape via the alarm systems, arming themselves with what appear to be SMG's (Submachine guns). Lucy now makes her way through the base's many hallways and elevators, naked as the day she was born, painting the various rooms with the blood and body parts of the guards trying to stop her. The vectors she has appear to act as a shield as well, blocking the bullets from the small caliber weaponry of the security teams. When she reaches one of the final elevators to the base, she is "greeted" by Director Kurama, one of the head hancho's of the facility, and about two dozen armed security guards all waiting outside the elevator. After killing an unlucky receptionist and using her body as a human shield, Lucy makes her way through the guards, who only stopped shooting because they ran out of ammo. The guards scatter, but Lucy manages to kill a few of them before they all get away. The director, however, does not move. He can only sneer and growl at Lucy as she walks by him, a bloody hand print on his back from her vectors suggest that Lucy could have killed him, but for some reason or another, changed her mind. It is at this time the director radios for the base to lock down the base and seal her up, naturally they follow orders, but someone in the control room has opened one of the exterior gates, allowing Lucy to slip out of the base towards the sea. Kurama can't take any chances, he has to take Lucy down, so he calls in a sniper. This sniper is not armed with one of the pea shooters the other guards were armed with, but a .50 caliber sniper rifle, the kind they use on tanks. The sniper fires on Lucy as she walks out onto the rocks, but the bullet doesn't hit properly. It does however, make contact, a blood trail confirming the bullet's entrance into Lucy's head, forcing her to fall into the cold water below.

This is when we meet Kouta and Yuka, two college students. Yuka is Kouta's cousin and she has a huge crush on him, even when they were little. After meeting up with him and reintroducing herself (They haven't seen each other in years) Yuka suggests they head to the beach to catch up on old times. After reaching the beach and reminiscing about Kouta's dead sister, he and Yuka notice a nude, underaged girl standing out in the water, Lucy. After a quick personality change, Lucy notices the duo looking at her with rather confused faces. She quickly tries to run away, but falls face first into the sand. After turning on the waterworks, Lucy gains the sympathy of Yuka, who forces Kouta to surrender his shirt so Lucy has something to wear. The two quickly conclude that Lucy does not speak their language, the only thing she's said so far being "nyu". Once they notice her horns, one of Kouta's childhood memories begins to come back, but before he can fully recover it, he is interrupted by Yuka suggesting that they take Lucy to Kouta's place, the Maple Inn. Upon reaching the Inn, Yuka and Kouta decide to give Lucy the name Nyu, because that's the sound she's always making. Now each of her personalities has a name, there's Lucy the deranged killer, and Nyu, the carefree, childish teenager.

Back at the facility where Lucy escaped, they are assessing the damages that she caused, and this is where Director Kurama makes it clear that he wants Lucy found and killed, not captured. He decides to call in the Special Assault Team, or SAT. This team of specialists is quickly assembled, one of it's members, Bando, being on the unstable side. Bando is a weird kind of guy, he's really unpredictable and gun-ho about things (he even hits women without a moment's notice) and he seems really eager to go out and kill Lucy. Back at the Maple inn, where Yuka, Kouta, and Nyu (AKA Lucy) are enjoying dinner, things take a turn for the worst then Kouta decides to take a stroll down memory lane. He shows Nyu and Yuka a seashell his sister found and gave to him when they were kids, right before she died. Nyu takes note of how unhappy Kouta looks as he's holding this sea shell, so she takes it from him and breaks it into pieces. This makes Kouta lose it, he flips out on Nyu, calling her every name in the book and demanding that she get out. Yuka tries to calm him down, but is unsuccessful as the sobbing Nyu runs out of the Inn, and into the night. She runs back to the beach where Kouta and Yuka found her, feeling terrible for what she did to Kouta's sea shell. She now stands looking out into the water, the rain pouring down on her, and the SAT ready to being it's search to find and kill her. This is the end of episode one .