The Atlanta Journal Constitution describes Gödel, Escher, Bach (GEB) as "A huge, sprawling literary marvel, a philosophy book, disguised as a book of entertainment, disguised as a book of instruction." That is the best one line description of this book that anybody could give. GEB is without a doubt the most interesting mathematical book that I have ever read, quickly making its place into the Top 5 books I have ever read.
The introduction of the book, "Introduction: A Musico-Logical Offering" begins by quickly discussing the three main participants in the book, Gödel, Escher, and Bach. Gödel was a mathematician who founded Gödel's Incompleteness Theorem, which states, as Hofstadter paraphrases, "All consistent axiomatic formulations of number theory include undecidable propositions." This is what Hofstadter calls the pearl. This is one example of one of the recurring themes in GEB, strange loops.
Strange loops occur when you move up or down in a hierarchical manner and eventually end up exactly where you started. The first example of a strange loop comes from Bach's Endlessly rising canon. This is a musical piece that continues to rise in key, modulating through the entire chromatic scale, ending at the same key with which he began. To emphasize the loop Bach wrote in the margin, "As the modulation rises, so may the King's Glory."
The third loop in the introduction comes from an artist, Escher. Escher is famous for his paintings of paradoxes. A good example is his Waterfall; Hofstadter gives many examples of Escher's work, which truly exemplify the strange loop phenomenon.
One feature of GEB, which I was particularly fond of, is the 'little stories' in between each chapter of the book. These stories which star Achilles and the Tortoise of Lewis Carroll fame, are illustrations of the points which Hofstadter brings out in the chapters. They also serve as a guidepost to the careful reader who finds clues buried inside of these sections. Hofstadter introduces these stories by reproducing "What the Tortoise Said to Achilles" by Lewis Carroll. This illustrates Zeno's paradox, another example of a strange loop.
In GEB Hofstadter comments on the trouble author's have with people skipping to the end of the book and reading the ending. He suggests that a solution to this would be to print a series of blank pages at the end, but then the reader would turn through the blank pages and find the last one with text on it. So he says to print gibberish throughout those blank pages, again a human would be smart enough to find the end of the gibberish and read there. He finally suggests that authors need to write many pages more of text than the book requires just fooling the reader into having to read the entire book. Perhaps Hofstadter employs this technique.
GEB is in itself a strange loop. It talks about the interconnectedness of things always getting more and more in depth about the topic at hand. However you are frequently brought back to the same point, similarly to Escher's paintings, Bach's rising canon, and Gödel's Incompleteness theorem. A book, which is filled with puzzles and riddles for the reader to find and answer, GEB, is a magnificently captivating book.