The way the episodes in Serial Experiments Lain are called is "layers". This is most likely in reference to the OSI model's concept of layers in regards to internet traffic. The anime consists of 13 episodes, that have been released throughout 1998, starting in early July and ending in late September. As of writing this, there's 13 episodes of Serial Experiments Lain, that I'll try to summarize later on in this text.
LAYER 01 - WEIRD
People are getting emails from a girl, Chisa Yomoda, who killed herself last week, which claim that she only gave up her body, but is actually still alive inside The Wired and that God is also there. After getting one of these emails, the introverted Lain Iwakura becomes interested in computers and asks her father for a new Navi.
LAYER 02 - GIRLS
Alice, Juri, and Reika talk to Lain saying they saw her during their first visit to the hardcore techno club 'Cyberia', but with a far more vigorous and forceful personality. After some persuasion, Lain decides to join Alice and her friends who are at Cyberia again to disprove that it was her. However, Lain becomes involved with a shooting in the club by a man under the influence of the micro-machine drug Accela.
LAYER 03 - PSYCHE
Lain has questions about a computer chip someone left in her locker, and her Dad's not talking. Some kids at the club say they know all about it - but they want a piece of Lain's wired wild side.
LAYER 04 - RELIGION
The more involved with computers she becomes, the more Lain begins to transform. In the cybernetic cocoon that was once her room, she's hard at work blurring the lines between reality and the wired.
LAYER 05 - DISTORTION
Lain's friends suspect her involvement in a series of computer errors that caused a lethal traffic accident. Meanwhile, her sister is haunted by mysterious messages demanding that she "fulfill the prophecy".
LAYER 06 - KIDS
When an image of herself appears in the clouds, the real Lain enters the wired on a search for answers. Her quest leads to a "child-killer" scientist whose devious work is being exploited by the Knights.
LAYER 07 - SOCIETY
Covert agents in black suits take Lain in for questioning. When the interrogation hits too close to home, Lain flips from real to wired in the blink of an eye.
LAYER 08 - RUMORS
Lain's unsavory behavior within the wired turns her into an outcast at school. Confused and alone, Lain investigates her own cyber-lifestyle only to be shocked by a voyeuristic incarnation of herself.
LAYER 09 - PROTOCOL
A DJ at the club passes Lain a plain brown envelope containing a computer chip of unknown origins. Hoping to learn more about the clandestine technology, Lain abducts a young boy for a "date."
LAYER 10 - LOVE
Lain encounters a man who call himself the ''god of the wired'', and members of the Knights all across the world log on to participate in a cryptic mass suicide.
LAYER 11 - INFORNOGRAPHY
Lain risks a meltdown by uploading a Navi clone into her own brain. Later, the border between reality and the wired is threatened when Lain forces the world forget a secret that never should have been revealed.
LAYER 12 - LANDSCAPE
"God" preaches that our bodies are simply an obstacle preventing the evolution of mankind. An exhausted Lain appears willing to sacrifice her own flesh and blood until Alice convinces her to take a stand against the digitalized deity.
LAYER 13 - EGO
Lain's guilt over the havoc caused by her interaction within the wired provokes her to take drastic - and irreversible - action.