After 116 years, Edwin Abbott Abbott's Flatland is still the best introduction to the method of analogy used by virtually all mathematicians and physicists when describing the fourth dimension. In recent years there have been more than a dozen new editions in English, and translations into at least nine foreign languages. For an article that provides background into the social satire of Flatland, see here..
Wait a minute! Wasn't "Flatland" sexist? The answer, everyone will be happy to know, is "No". The place Flatland was a sexist society, but the book "Flatland" is intended, and was received, as social satire and more. Its author was highly regarded as an educational reformer hailed by the premier women educators as a leader in the movement to bring educational opportunities to young women in Victorian England. For more information, see the section on social satire in the Princeton Science Series edition of "Flatland", with an introduction by Thomas Banchoff.
A recent exhibit, Flatland: A Millennial Book, which was hosted by the Brown University library as a physical display, is now available on the web as a virtual experience.
Many authors cite Edwin Abbott Abbott as one of their first inspirations in the study of abstract mathematics, particularly in higher dimensions. One of these is Prof. Dirk Struik , who, at this writing, is 105 years old. Here is a picture of him giving a lecture on his hundredth birthday. For the related story, go here . Here is his reference to Flatland in his classic book Lectures in Classical Differential Geometry.
Wonderful news is the impending reissue of one of the best books about life in a modern two-dimensional universe, namely "The Planiverse" by A. K. Dewdney, featuring the hero of the story, Yendred . Here is information on ordering your copy of The Planiverse.
Much of the popularity of "Flatland" in the US is thanks to Hayward Cirker, founder of Dover Publications, who passed away in March of this year. In 1952, he personally chose this as one of his first titles in mathematics. Here is a poster advertising that very first Dover edition. Since that time, it has remained one of their best sellers. Seven years ago, "Flatland" appeared as a Dover Thrift Edition, selling for $1, and guaranteeing that it will remain a favorite of teachers and students for some time to come. The Dover editions have sold more than half a million copies.
To see a fine treatment of many of the themes from "Flatland" and an introduction to the world of higher-dimensional "polytopes", see this final project by two freshmen and a junior, all from Paideia School in Atlanta GA.
For an excellent site showing the slices not only of the Hypercube but also other regular figures in four-dimensional space, see the site of Mark Newbold. This site also contains a bibliography of additional links.
Here is another good site on regular polytopes in higher dimensions, and another featuring rotating stereo images.. The classic reference in this field is "Regular Polytopes" by Prof. H.S.M. Coxeter still in print as a Dover paperback.