I'm not sure why the subtitle contains the word 'romance'.
This book reminded me of Star Maker, but luckily Flatland is much shorter and consists of beautiful English prose. Flatland is a monologue describing an epiphany concerning the Nature of the Universe. I also see connections with thought experiments such as Plato's allegory of the cave. It invites the reader to extend the analogy to our own experience.
The tone of the narrator is scientific and slightly sad, which makes it (despite its short length) a bit of a heavy read. There's also a distopian tinge to the story.
The Flatland States are conservative and very woman-unfriendly. Can't tell if the writer is a bigot or a satirist. ;)
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This is a fascinating little book. Written in the latish 19th century, it is a despatch from a very simple two-dimensional world by one of its inhabitants, the supposed author: A Square. The first part of the book simply describes the society of Flatland for the benefit of we three-dimensional creatures, its intended audience. The second describes how the square came to learn of our three-dimensional world, as well as other zero- and one-dimensional worlds, and his efforts to educate his fellow bi-dimensional fellows about the higher dimensions.

Both sections are very different (the first has little plot, and more of the maths; the second is much more philosophical), but both are packed with allusions and layers of meaning. For example, the society shows antediluvian, barely qualified, attitudes to women and class - this is a little off-putting initially, until it becomes clear that this is social satire, of a Swiftian level. In describing his attempts to educate people about the higher-dimensions, Abbott is explicitly imploring the reader to be open-minded about radical abstract ideas, by way of making us consider that there are higher-dimensions of which we are not aware. And ultimately the story contains elements of traditional tragedy, of transformation - apotheosis even - and of attaining knowledge from a state of ignorance and of the resultant fall from grace.

On top of that, the book is crammed with references to Shakespeare and the classics. (And through all that it is written in beguilingly simple language (although in a slightly archaic style - even for the 19th century - to give it a timeless quality).

It is a deceptively simple, towering achievement.

This edition in particular is to be recommended. I found the notes on the maths, and Abbott's literary references very useful (although the ones explaining some of the language far less so). And almost more fascinating than Abbott's fable of abstract thought is the man that emerges in the other material in the book.

From the main text you discern a clever, thorough, drily witty and whimsical man; and the basic notes clearly illustrate through their detailing of classical and literary allusions, a highly - and widely - learned man; but that barely scratches the many surfaces of Abbott. Fortunately there is considerable back material in the appendices to fill in some of the detail. His accomplishments include

Legendary headmaster (Prime Minister Asquith attended the City of London School while Abbott was in charge)
An award-winning Cambridge scholar (top in his year in Classics)
A renowned preacher
A bible scholar and leading progressive thinker on the non-miraculous Jesus (reminiscent of Thomas Jefferson's 'The Life and Morals of Jesus of Nazare')
Shakespearean scholar
A biographer and critic of Cardinal Newman
Educational reformer (an early proponent of formal teacher training; promoting teaching for lower classes)
Active Proponent of women's education and suffrage
Admiree (reciprocated) of George Eliot
Author of numerous books and essays, on a range of topics encompassing most of the above

And, of course, a writer of whimsical mathematical fiction, which - along with beautifully communicated (and occasionally entertainingly illustrated) higher mathematical concepts - incorporates existentialism, social criticism, and a plea for scientific rigour and open-mindedness.

I have a new hero.
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Delightful and thought-provoking for a twelve-year-old. One of those classic books from which everyone can absorb deep and lasting ideas. ( )

This was pretty amazing. 1800 style writing and talking geometry, what is not to like? Ultimately the readability suffers under these two characteristics, but Abott wrote a pretty interesting short story regardless. For anyone who doesn't want to go through 80 pages of "doths" and "thy's" I cannot recommend the 2007 Ehlinger movie Flatland enough. ( )

Probably quite revolutionary for its time, but if issues of classism and sexism bother you, then you may find this book irritating. Doesn't take much time to read, though, so if nothing else, it prompts an interesting thought exercise about the possibility of conceiving ideas that one doesn't actually have the senses to view. ( )