In the spirit of Edwin Abbott Abbott's Flatland, Dewdney and his computer science students designed a vertical 2D world (i.e. East-West and Up-Down, no N-S) and considered the issues of biology and society for the inhabitants.
To their surprise, they find their artificial 2D universe has somehow accidentally become a means of communication with an actual 2D world - Arde. They make a sort of "telepathic" contact with "YNDRD," referred to by the students as Yendred, a highly philosophical Ardean (or Nsana, as they call themselves), as he begins a journey across the single continent Ajem Kollosh to learn more about a mysterious philosophy the inhabitants of his destination have.
The students and narrator communicate with Yendred by typing on the keyboard, and Yendred describes how he "feels" their thoughts in his head. For Yendred's replies, he thinks an answer, and it appears on the computer's printout. Yendred's name is actually "Dewdney" reversed, or "Yendwed", as spoken by one of the students with a speech impediment.
Written as a travelogue, Yendred crosses the world to reveal its features, explaining to the students diverse topics such as the politics, geography, construction (all houses are underground, for example, so as not to impede movement), tools (nails are useless for attaching two objects, tape and glue are used instead), biology (there is no digestive tract in most Ardean creatures, because of the danger of splitting into two, but evolution devised a solution), astronomy, and even games (such as Alak), all designed for 2D. An appendix explains some fundamentals of Ardean two-dimensional physics and chemistry.
Hidden under the surface of this scientific and technological tale is a Sufi allegory. Yendred is on a spiritual quest, which brings him to a square shrine (the 2D equivalent of the Muslim Kaaba in Mecca), situated between the religious East and the secular West. Here he meets a sage who is able to move in the third dimension. At this point Yendred severs contact with the students and narrator. Clues to the real meaning of the book lie in the Arabic words that are scattered through it, for example Arde is ard, 'earth'; Nsana is insan, 'human'; Ajem Kollosh is ajm kull shay, 'home of everything' and so on. Dewdney chose Maltese Arabic as being intermediate between East and West.