In the 21st century, aliens have arrived on Earth and live among humans. In sleepy Enohana, the dirt-poor student Chigasaki Mayuko finds herself living together with NieA, a low-caste ("Under Seven") alien. While Mayuko struggles diligently to make ends meet, NieA seems to be totally unconcerned with the consequences of her actions.

Alien attempts to learn about modern society by asking questions.

Pochiyama-san works at a local pharmacy. She is a loner and seldom speaks; instead she writes what she wants to say on... well you'll see for yourself once you read this short and humorous one-shot.
(Source: Mangaupdates)
Four installments have been released to date, once every year since 2005. The fourth and most recent was published on 30 December 2008. The first three installments were published together as an internationally available iPod Touch / iPhone app (with a rather poorly-made official English translation) via the iTunes App Store on 14 August 2008.

A girl wakes up in an unknown world all alone. In this world she sees another girl who is her exact twin. Their names: 328 and 329. There is only running water; no food anywhere. In their search for food, they find a raft to take them beyond this unknown place, but it becomes evident that only one person will be able to board this raft. The annoying buzzing sounds and voices of a winged insect, the craving for food, and the desire to leave will push them to the brink. One of them will snap...

Eshikawa receives a letter from parents of a former girlfriend Hasumi, which says that she committed suicide. He remembers the time when they were together and trying to understand why she had committed suicide.

from wiki:

The series follow a young girl named Rakka, a newly arrived haibane (an angelic-looking being), and other characters in the city of Glie (guri), a walled city with one entrance where no one is allowed to leave.

Also contains a side story written after the end of the anime. It shows the relation between Reki and Nemu (and Hyouko) after the departure of Kuramori. The colour illustrations are those supposedly by Reki. One is a scenery in her dream and the other is the portrait of Kuramori.

The daily life of a girl nicknamed Ryuushika with a wild imagination.

The Nightmare of Fabrication is a beautifully drawn full-colour manga from Yoshitoshi ABe. The 18 page short story can be found in the Lain Omnipresence in Wired artbook. It's a bonus story which apparently isn't related with neither the anime nor the PS game. It shows characters who were included in the PS game but not in the TV series (like the psychiatrist), but also determinant characters from the anime who didn't appear in the videogame (like Deus).